Question

Help!!! Find the lateral surface area of the following square pyramid:

Answer 1

Given:

A square base pyramid with base length 6 cm and the slant height is 4 cm.

To find:

The lateral surface area of the given square pyramid.

Solution:

The lateral surface area of the given square pyramid is equal to the areas of 4 congruent triangles with base 6 cm and height 4 cm.

Area of a triangle is:

$Area=\dfrac{1}{2}\times base\times height$

So, the area of one triangle or one side of the given pyramid is:

$A_1=\dfrac{1}{2}\times 6\times 4$

$A_1=\dfrac{24}{2}$

$A_1=12$

Now, the lateral surface area of the given square pyramid is 4 times the area of one triangle.

$LA=4A_1$

$LA=4(12)$

$LA=48$

Therefore, the lateral surface area of the given square pyramid is 48 cm².