## Introduction

In geometry, a **pyramid** is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex forms a triangle. It is a conic solid with polygonal base.

If the base of a pyramid is rectangle, then the pyramid is called as rectangular pyramid. (Source: From Wikipedia).

## Formula to Find the Surface Area of a Rectangular Pyramid

Surface area of a rectangular pyramid is the sum of areas of all surfaces of the rectangular pyramid. It can be shown graphically as follows,

The surface area of the rectangular pyramid = Area of the base rectangle + 2(area of pair of opposite triangles)

In rectangular pyramid, we have two different triangles, because of the length and breadth of the base rectangle.

## Example Problem to Find the Surface Area of Rectangular Pyramid

**Example problem**

Find the surface area of the rectangular pyramid in the given diagram. (All units in m)

**Solution**

**Area of the base rectangle** = bh

= 6 * 4

= 24 m^{2}

Now we have to find the area of the triangles, Here we have two pair of different triangles

A pair of triangles with base 6 m and another pair of triangles with base 4 m.

**Area of triangles with base 4 m**:

To find the area of triangles with base 4, we need the perpendicular height. The perpendicular height can be found by the height of the pyramid (8 m) using **Pythagoras theorem**.

h^{2} = 8^{2} + 3^{2}

h^{2} = 64 + 9

h^{2} = 73

h = `sqrt(73)`

Area of the triangle with base 4 m = `1/2` * 4 * `sqrt(73)`

= `2sqrt(73)`

**Area of the triangle with base 6 m:**

Here,

h^{2} = 8^{2} + 2^{2}

h^{2} = 64 + 4

h^{2 }= 68

h = `sqrt(68)`

Area of the triangle with base 6 m = `1/2` * 6 * `sqrt(68)`

= 3 * `2sqrt(17)`

= `6sqrt(17)`

So, the surface area of the rectangular pyramid is given by,

SA = area of the base + 2(area of the triangle with base 4 m) + 2area of the triangle with base 6 m)

= 24 + `2(2sqrt(73))` + `2(6sqrt(17))`

=24 + `4sqrt(73)` + `12sqrt(17)`

= `4(8 + sqrt(73) + 3sqrt(17))` square m

So, the surface area of the rectangular pyramid = `4(8 + sqrt(73) + 3sqrt(17))` square meter.

## 3 comments ↓

There are no comments yet...Kick things off by filling out the form below..