Answer:
the answer is option (B) 105 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 25 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(25 in²) = 5 in
Therefore, the length of one side of the base is 5 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 5 in. The height is given as 8 in.
Area = 1/2 * 5 in * 8 in = 20 in²
So the area of one triangular face is 20 in².
The total surface area of the pyramid is:
Surface area = 4 * 20 in² + 25 in² = 105 in²
Therefore, the surface area of the pyramid is 105 in².
So the answer is option (B) 105 in².