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](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20square%7D%3Da%5E2)
Area of square with side length 6 cm is
![\text{Area of square}=(6)^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20square%7D%3D%286%29%5E2)
![\text{Area of square}=36](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20square%7D%3D36)
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](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20a%20triangle%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20base%5Ctimes%20height)
Area of each triangular surface is
![\text{Area of each triangular surface}=\dfrac{1}{2}\times (6)\times (4)](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20each%20triangular%20surface%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20%286%29%5Ctimes%20%284%29)
![\text{Area of each triangular surface}=12](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20each%20triangular%20surface%7D%3D12)
Total area of 4 triangular surfaces is
![\text{Area of 4 triangular surfaces}=4\times 12](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%204%20triangular%20surfaces%7D%3D4%5Ctimes%2012)
![\text{Area of 4 triangular surfaces}=48](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%204%20triangular%20surfaces%7D%3D48)
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](https://tex.z-dn.net/?f=Area%3D36%2B48)
![Area=84](https://tex.z-dn.net/?f=Area%3D84)
Therefore, the area of given square pyramid is 84 cm².