Surface Area of Rectangular Pyramid

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,

Rectangular pyramid

Rectangular pyramid

 

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)

surface area of the rectangular pyramid

Rectangular Pyramid

 

Solution

Area of the base rectangle = bh

= 6 * 4

= 24 m2

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.

surface area of the rectangular pyramid

Rectangular Pyramid

 

h2 = 82 + 32

h2 = 64 + 9

h2 = 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,

h2 = 82 + 22

h2 = 64 + 4

h= 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..

Leave a Comment