# Rectangular Pyramid - Definition, Properties, Types, Formulas, Examples (2023)

A rectangular pyramid is a type of pyramid with the base shaped like a rectangle but the sides are shaped like a triangle. A pyramid usually has triangular sides but with different bases such as a square pyramid or a hexagonal pyramid. The distinguishing factor among all these pyramids is the base, the face, the edges, and vertices. A rectangular pyramid has its own properties and formulas. Let us learn more about the rectangular pyramid and solve a few examples.

 1 Definition of Rectangular Pyramid 2 Properties of Rectangular Pyramid 3 Types of Rectangular Pyramid 4 Volume of Rectangular Pyramid 5 Total Surface Area of Rectangular Pyramid 6 Rectangular Pyramid Net 7 FAQs on Rectangular Pyramid

## Definition of Rectangular Pyramid

A rectangular pyramid is a 3-D object with a base shaped like a rectangle and triangle-shaped faces or sides that correspond to each side of the base. Like the other types of pyramids, a rectangular pyramid also has a point on top of the base of the pyramid that is joined together by bringing the top of all the sides which is known as the apex. A rectangular pyramid has a total of 5 faces, 5 vertices, and 8 edges and is of two types a right pyramid or an oblique pyramid. The base and the sides of the pyramid are joined at the vertex. The image below interprets the shape of the pyramid. ## Properties of Rectangular Pyramid

Every pyramid has its own properties that make it different from one another. A rectangular pyramid is unique in its shape due to its properties. Let us look at what they are:

• A rectangular pyramid has 5 faces, 5 vertices, and 8 edges.
• One face is the rectangle base and 4 are in the shape of a triangle.
• All the triangular faces are congruent to the opposite face.
• One of the vertexes meet at the apex which is right above the base of the pyramid.
• The vertex is the intersection point between the base and the side and four edges are the intersection point at the base.
• 4 edges formed above the base of the pyramid, make the slope. While the other 4 edges are at the base.

## Types of Rectangular Pyramid

There are two types of rectangular pyramids namely - the right rectangular pyramid and the oblique rectangular pyramid.

### Right Rectangular Pyramid

If the apex of the rectangular pyramid is right above the center of the base, it forms a perpendicular to the base, which marks its height. Such a rectangular pyramid is called the right rectangular pyramid. When a rectangular pyramid is mentioned, it is usually referred to as the right rectangular pyramid.

(Video) What is a Pyramid? | Types of Pyramids | Don't Memorise ### Oblique Rectangular Pyramid

If the apex of the rectangular pyramid is not aligned right above the center of the base, the pyramid is called an oblique rectangular pyramid. This type of pyramid appears to have tilted. Thus, in the case of an oblique rectangular pyramid, height is taken as the length of the perpendicular drawn apex to the base of the pyramid. ## Volume of Rectangular Pyramid

The volume of the rectangular pyramid is defined as the capacity of the rectangular pyramid and is the number of unit cubes that can fit into it. The unit of volume is cubic units. For example, it can be expressed as m3, cm3, in3, etc. depending upon the given units. The formula to find the volume of a rectangular pyramid is:

Volume = 1/3 × Base Area × h

Where,

• h is the perpendicular height
• base area = Length of the rectangular base × Width of the rectangular base.

The volume of the rectangular pyramid can be found by finding the length, width, and height after which the measurements can be placed in the above-mentioned formula. (Video) What is the surface area formula for a rectangular pyramid?

## Total Surface Area of Rectangular Pyramid

The total surface area of a rectangular pyramid is the sum of the areas of its base and its lateral faces. It is calculated by adding up the area of all rectangular and triangular faces. The important aspects to remember where finding the total surface area are: area of the rectangular base, area of front and back identical triangles, slant height, and area of side triangles. The combination of all these aspects will help in finding the total surface area of a rectangular pyramid. The formula for each of these aspects and the steps are:

1. Area of the rectangular base = length of the rectangular base × width of the rectangular base.

2. Area of front and back identical triangles = $$l \sqrt{\left(\frac{\text{width of rectangular base}}{2}\right)^{2}+(\text {height of pyramid})^{2}}$$. Since the area of the two front and back triangles is- [2 × 1/2(base)(height)].

3. Slant height of the triangles = $$\sqrt{\left(\frac{\text{width of rectangular base}}{2}\right)^{2}+({\text {height of pyramid}})^{2}}$$

4. The side triangles' area can be found similar to the front and back triangles, only the slant height formula is changed:

$$w \sqrt{\left(\frac{\text{length of rectangular side}}{2}\right)^{2}+({\text {height of pyramid}})^{2}}$$

where, the slant height is $$\sqrt{\left(\frac{\text{length of rectangular side}}{2}\right)^{2}+({\text {height of pyramid}})^{2}}$$.

Therefore, the total surface area of a rectangular pyramid is calculated by adding all the areas together which become:

(Video) How Many Faces, Edges And Vertices Does A Square Pyramid Have?

A = lw +l √[(w/2)2 + h2] + w√[(l/2)2 + h2] square units

### Lateral Surface Area of Rectangular Pyramid

The lateral surface area of any object is calculated by removing the base area or we can say that the lateral surface area is the area of the non-base faces only. Once the rectangular area is removed from the total surface area formula we derive the lateral surface area formula. Thus, the lateral surface area of a rectangular pyramid is l √[(w/2)2 + h2] + w√[(l/2)2 + h2]
where,

• l = Length of the rectangular base
• w = Width of the rectangular base
• h = Height of the pyramid

## Rectangular Pyramid Net

The net of a rectangular pyramid consists of 4 triangular faces and 1 rectangular base. This is seen when the shape of the pyramid is opened i.e. when the object goes from 3D to 2D. The apex is opened making the triangle faces flattened. The below image shows the net of a rectangular pyramid. ### Related Topics

Listed below are a few interesting topics related to the rectangular pyramid, take a look.

• Triangular Pyramid
• Rectangular Pyramid Volume Calculator
• Square Pyramid

## FAQs on Rectangular Pyramid

### What is a Rectangular Pyramid?

A rectangular pyramid is a 3-D object with a base shaped like a rectangle and triangle-shaped faces or sides that correspond to each side of the base. The top of the base of the pyramid that is joined together by bringing the top of all the sides is known as the apex. A rectangular pyramid has a total of 5 faces, 5 vertices, and 8 edges and is of two types a right pyramid or an oblique pyramid. The base and the sides of the pyramid are joined at the vertex.

(Video) Prisms and Pyramids | Grade 3 & 4 Math | TutWay

### How Many Faces, Edges, and Vertices does a Rectangular Pyramid Have?

A rectangular pyramid consists of 5 faces, 5 vertices, and 8 edges. One of the faces is the rectangular base whereas the rest 4 are the triangles. 4 edges of the rectangular pyramid that are joined by the triangular sides are considered as the slope of the rectangular pyramid.

### What are the Two Types of Rectangular Pyramid?

The two types of the rectangular pyramid are:

• Right Rectangular Pyramid: If the apex of the rectangular pyramid is aligned right above the center of the base, the pyramid is called a right rectangular pyramid.
• Oblique Rectangular Pyramid: If the apex of the rectangular pyramid is not aligned right above the center of the base, the pyramid is called an oblique rectangular pyramid.

### How Do You Find the Volume of a Rectangular Pyramid?

The volume (V) of a rectangular pyramid can be easily found out by just knowing the base area and its height and putting the values of these dimensions in the formula, V = 1/3 × Base Area × Height. Where base area = length × width of the rectangular pyramid.

### What is the Formula to Calculate the Total Surface Area of a Rectangular Pyramid?

The total surface area of a rectangular pyramid formula using the base width, length, and height is given as, T.S.A. = lw + l√[(w/2)2 + h2] + w√[(l/2)2 + h2].

where,

• l is length of the rectangular base.
• w is width of the rectangular base.
• h is height.

### What is the Formula to Calculate the Lateral Surface of a Rectangular Pyramid?

The lateral surface of a rectangular pyramid is calculated by l √[(w/2)2 + h2] + w√[(l/2)2 + h2].

where,

• l is length of the rectangular base.
• w is width of the rectangular base.
• h is height.

### What is the Net of a Rectangular Pyramid?

The net of a rectangular pyramid is consists of 4 triangular faces and 1 rectangular base. When the pyramid is flattened out, the triangles and rectangle can be seen clearly.

## FAQs

### Rectangular Pyramid - Definition, Properties, Types, Formulas, Examples? ›

The area of the base = Length × Width = 12 × 10 = 120 in2. Putting the values: Base area = 120 and h = 20 in the formula. V = 1/3 × 120 × 20 = 800 in3.

What is the formula for rectangular pyramids? ›

Volume of rectangular pyramid = 1 3 × length × width × height.

What are the properties of a rectangular pyramid? ›

Rectangular pyramid properties
• 5 faces, 5 vertices, and eight edges make up a rectangular pyramid.
• One face has a rectangle basis, while the remaining four have a triangle shape.
• All of the triangle faces are congruent with the opposite face.

What is an example of a rectangular pyramid? ›

The pyramids in Egypt are rectangular pyramids.

What is the example formula of pyramid? ›

The general formula for the total surface area of a regular pyramid is given as: The Total surface area of a pyramid formula = ½ pl + B, Where 'p' is the perimeter of the base and 'l' is the slant height of the pyramid and B is the area of the base.

Where is the pyramid formula? ›

SA=B+12(P×l), where B is the area of the base of the pyramid, P is the perimeter of the base, and l is the slant height of the pyramid. We can find B by using the formula 12bh for area of a triangle. P can easily be determined by adding up the lengths of the sides of the base triangle.

What is the formula for calculating pyramid? ›

What Is the Formula To Find the Volume of Pyramid? The volume of a pyramid is found using the formula V = (1/3) Bh, where 'B' is the base area and 'h' is the height of the pyramid. As we know the base of a pyramid is any polygon, we can apply the area of polygons formulas to find 'B'.

What is the definition of a rectangular pyramid? ›

A rectangular pyramid is a solid with a rectangle-shaped base and triangular lateral faces. The base of a rectangular pyramid is rectangular, but the lateral faces are triangular. The sides of a pyramid are usually triangular, but the base can be a square or hexagonal in shape.

What are the properties of a rectangular? ›

What are the two properties of rectangular? ›

Properties of Rectangle

Each vertex has angle equal to 90 degrees. The opposite sides are equal and parallel. Diagonal bisect each other.

### What are 5 examples of rectangular prism? ›

It has three dimensions, length, width, and height. Some examples of a rectangular prism in real life are rectangular tissue boxes, school notebooks, laptops, fish tanks, large structures such as cargo containers, rooms, storage sheds, etc.

What is the formula to rectangular prism? ›

It is given by the formula, 2(lw + wh + hl), where l is length, w is width, and h is the height of the rectangular prism.

What are the parts of a rectangular pyramid? ›

Faces, Edges and Vertices

Faces: A rectangular pyramid has a total of five faces. One face is its rectangular base and the rest four faces are its four triangular-shaped faces. All the triangular faces here are congruent to the opposite triangular face.

What are properties of a pyramid? ›

A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex. A pyramid is formed by connecting the bases to an apex. Each edge of the base is connected to the apex, and forms the triangular face, called the lateral face.

What are 5 examples of pyramids shape? ›

Depending on the base, a pyramid can be of different shapes. Some common types are: triangular, rectangular, square, pentagonal, hexagonal.

What is a pyramid in math? ›

A pyramid is a three-dimensional figure. It has a flat polygon base. All the other faces are triangles and are called lateral faces. The number of lateral faces equals the number of sides on its base. Its edges are the line segments formed by two intersecting faces.

Do pyramids have 3 or 4 sides? ›

The base of the Great Pyramid of Giza is a square, right? Well, not quite. Despite what you may think about this ancient structure, the Great Pyramid is an eight-sided figure, not a four-sided figure. Each of the pyramid's four side are evenly split from base to tip by very subtle concave indentations.

What is the mathematical formula? ›

What is Formula in Math? The formula is a fact or a rule written with mathematical symbols. It usually connects two or more quantities with an equal sign. When you know the value of one quantity, you can find the value of the other using the formula. It helps to solve the questions quickly.

What are the formulas for square pyramids? ›

1] Square Pyramid

The Square Pyramid formulas are, Base Area of a Square Pyramid = b. Surface Area of a Square Pyramid = 2 × b × s +b. Volume of a Square Pyramid=\frac{1}{3} × b2 × h.

What is the formula for the slant height of a pyramid? ›

The Pythagorean theorem, a2 + b2 = c2, can be used to compute the slant height. The height of the altitude will be both for cones and pyramids, and the slant height will be c.

### What is the formula for the surface area of a rectangular pyramid? ›

Hence, the surface area and volume of the rectangular pyramid are L + B × H 2 + L 2 2 + L × B and L × B × H 3 respectively.

How many edges are in a rectangular pyramid? ›

A rectangular pyramid has 5 faces. Its base is a rectangle or a square and the other 4 faces are triangles. It has 8 edges and 5 vertices. and four vertices.

What are the properties and formula of a rectangle? ›

If the length of the rectangle is L and breadth is B then, Area of a rectangle = Length × Breadth or L × B. Perimeter of rectangle = 2 × (L + B)

What is the definition of a rectangle with example? ›

A square is a shape that has four equal length sides and four 90 degree right angles. A rectangle is a shape with four straight sides and four right angles. That means that by definition, a square can be classed as a rectangle.

What are the different types of rectangles? ›

Two special types of rectangles are the square and Fibonacci rectangle. The square is a special rectangle with four equal sides along with four right angles. Fibonacci's rectangle is a rectangle whose ratio between the length and width is 1.618.

What are the types of rectangles? ›

What is not a property of a rectangle? ›

There is no rule that the diagonals of the rectangle are perpendicular to each other.

What are 5 rectangular numbers? ›

Types of Rectangular Numbers

The first type of rectangular numbers would create a very specific list of numbers. This list would be: 2, 6, 12, 20, 30, 42, 56, 72, 90....

What is the formula for the area of a prism? ›

The formula for the surface area of a prism is [Math Error] S A = 2 B + p h , where B, again, stands for the area of the base, p represents the perimeter of the base, and h stands for the height of the prism.

What are 3 examples of a prism? ›

Examples include square prisms, rectangular prisms, triangular prisms and octagonal prisms. Because a prism must include flat sides, a cylinder isn't a prism.

### What is rectangular formula? ›

The formula for the Area of a Rectangle. Area of a Rectangle. A = l × b. The area of any rectangle is calculated, once its length and width are known. By multiplying length and breadth, the rectangle's area will obtain in a square-unit dimension.

What is the formula of a rectangular shape? ›

The area of a rectangle = length × width .

What is a rectangular equation? ›

A rectangular equation, or an equation in rectangular form is an equation composed of variables like x and y which can be graphed on a regular Cartesian plane. For example y=4x+3 is a rectangular equation.

What are the 3 parts of a pyramid? ›

A polyhedron that has a polygonal base and triangles for sides, is a pyramid. The three main parts of any pyramid's: apex, face and base.

Which figure is a rectangular prism? ›

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.

What is pyramid and its types? ›

The three types of ecological pyramids include: Pyramid of Number. Pyramid of Biomass. Pyramid of Energy.

What are the 3 main pyramid shapes and their characteristics? ›

And while every population pyramid is unique, most can be categorized into three prototypical shapes: expansive (young and growing), constrictive (elderly and shrinking), and stationary (little or no population growth). Let's take a deeper dive into the trends these three shapes reveal about a population and its needs.

What type of structure is a pyramid? ›

A pyramid is a polyhedron for which the base is a polygon and all lateral faces are triangles. In this lesson, we'll only concern ourselves with pyramids whose lateral faces are congruent — that is, they're the same size and shape.

What is pyramid made of? ›

Why are there 3 pyramids? ›

The pyramids of Giza were royal tombs built for three different pharaohs. The northernmost and oldest pyramid of the group was built for Khufu (Greek: Cheops), the second king of the 4th dynasty. Called the Great Pyramid, it is the largest of the three.

### What's a 3 sided pyramid called? ›

A triangular pyramid is a pyramid having a triangular base. The tetrahedron is a triangular pyramid having congruent equilateral triangles for each of its faces.

What type of pyramid has 5 sides? ›

A square-based pyramid has 5 faces, 5 vertices including the apex and 8 edges.

What is a pyramid with 5 sides? ›

Like all pyramids, a pentagonal pyramid is a three-dimensional shape. It has its base as a pentagon. You already know that a pentagon is a polygon with five sides. In geometry, a pentagonal pyramid is a pyramid with a pentagon as a base upon which five triangles have raised that meet at a point.

What is the formula for rectangular prisms? ›

It is given by the formula, 2(lw + wh + hl), where l is length, w is width, and h is the height of the rectangular prism.

What is the formula in finding the surface area of a rectangular pyramid? ›

Total surface area of a rectangular pyramid = Area of the base rectangle + Lateral surface area of a pyramid.

What is the Egyptian formula for pyramid? ›

The volume equation for a square pyramid is V=\frac{1}{3}bh, where b is the area of the base and h is the height. For the Pyramid of Menkaure, we are given the height, and can find the area of the base by squaring the side length: V = \frac{1}{3}\times 339^2\times 215 \approx 8,240,000 \text{ feet}^3.

What is the formula of rectangular object? ›

length × width × height . The volume, V , of any rectangular solid is the product of the length, width, and height. We could also write the formula for volume of a rectangular solid in terms of the area of the base. The area of the base, B , is equal to length×width.

What is a rectangular pyramid in math? ›

A rectangular pyramid is a solid with a rectangle-shaped base and triangular lateral faces. The base of a rectangular pyramid is rectangular, but the lateral faces are triangular. The sides of a pyramid are usually triangular, but the base can be a square or hexagonal in shape.

What is the area and volume of a rectangular pyramid? ›

Hence, the surface area and volume of the rectangular pyramid are L + B × H 2 + L 2 2 + L × B and L × B × H 3 respectively.

How to calculate the volume of a truncated rectangular pyramid? ›

The formula for the volume of a truncated square pyramid with height h, and top edge a cm and bottom edge b cm is V = 1/3*(a2 + ab + b2)*h. (The derivation of this formula is given below!)

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