Step 1:
Concept: Calculate the area of each face and add all together to get the surface area of the pyramid.
The regular pyramid below have 4 triangles and a square
Step 2: Apply the area formula to find the area of the 4 triangles and a square.
[tex]\begin{gathered} \text{Area of a triangle = }\frac{Base\text{ x Height}}{2} \\ \text{Area of the square base = Length x Length} \end{gathered}[/tex]Step 3:
Given data for the triangle
Height = 21
Base = 12
[tex]\begin{gathered} Area\text{ of a triangle = }\frac{Base\text{ x Height}}{2} \\ =\text{ }\frac{21\text{ x 12}}{2} \\ =\text{ }\frac{252}{2} \\ =126\text{ sq. units} \\ \text{Area of the four triangles = 4 x 126 = 504 sq. units} \end{gathered}[/tex]Step 4: Find the area of the square
Given data for the square
Length = 12
Area = length x length = 12 x 12 = 144 sq. units
Step 5: Add the area of the four triangles and the square.
Surface area of the regular pyramid = 504 + 144
= 648 sq. units