Answer:
the answer is option (B) 84 in².
Explanation:
The surface area of a square pyramid can be calculated by finding the sum of the areas of the four triangular faces and the base.
The area of the base is given as 36 in². Since the base is a square, we can find the length of one side of the base by taking the square root of the area:
sqrt(36 in²) = 6 in
Therefore, the length of one side of the base is 6 in.
To find the area of one of the triangular faces, we can use the formula for the area of a triangle:
Area = 1/2 * base * height
In this case, the base is equal to the length of one side of the square base, or 6 in. The height is given as 4 in.
Area = 1/2 * 6 in * 4 in = 12 in²
So the area of one triangular face is 12 in².
The total surface area of the pyramid is:
Surface area = 4 * 12 in² + 36 in² = 84 in²
Therefore, the surface area of the pyramid is 84 in².
So the answer is option (B) 84 in².