Question

Find the total surface area of this square based pyramid

Answer 1

Given:

Length of a side of base of a square base pyramid = 6 cm

Height of each triangular surface = 4 cm.

To find:

The total surface area of the square based pyramid.

Solution:

Area of a square with side length a is

`\text{Area of square}=a^2`

Area of square with side length 6 cm is

`\text{Area of square}=(6)^2`

`\text{Area of square}=36`

So, area of square with side length 6 cm is 36 cm².

Area of triangle is

`\text{Area of a triangle}=(1)/(2)* base* height`

Area of each triangular surface is

`\text{Area of each triangular surface}=(1)/(2)* (6)* (4)`

`\text{Area of each triangular surface}=12`

Total area of 4 triangular surfaces is

`\text{Area of 4 triangular surfaces}=4* 12`

`\text{Area of 4 triangular surfaces}=48`

So, area of all triangular surfaces is 48 cm².

Now, total area of pyramid is the sum of base area and area of all triangular sides.

`Area=36+48`

`Area=84`

Therefore, the area of given square pyramid is 84 cm².