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

$\text{Area of a triangle}=\dfrac{1}{2}\times base\times height$

Area of each triangular surface is

$\text{Area of each triangular surface}=\dfrac{1}{2}\times (6)\times (4)$

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

Total area of 4 triangular surfaces is

$\text{Area of 4 triangular surfaces}=4\times 12$

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

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.