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
[tex]\text{Area of square}=a^2[/tex]
Area of square with side length 6 cm is
[tex]\text{Area of square}=(6)^2[/tex]
[tex]\text{Area of square}=36[/tex]
So, area of square with side length 6 cm is 36 cm².
Area of triangle is
[tex]\text{Area of a triangle}=\dfrac{1}{2}\times base\times height[/tex]
Area of each triangular surface is
[tex]\text{Area of each triangular surface}=\dfrac{1}{2}\times (6)\times (4)[/tex]
[tex]\text{Area of each triangular surface}=12[/tex]
Total area of 4 triangular surfaces is
[tex]\text{Area of 4 triangular surfaces}=4\times 12[/tex]
[tex]\text{Area of 4 triangular surfaces}=48[/tex]
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.
[tex]Area=36+48[/tex]
[tex]Area=84[/tex]
Therefore, the area of given square pyramid is 84 cm².