Answer:
the answer is (A) 72 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 perimeter of the base is given as 24 inches, which means that each side of the base has a length of 24/4 = 6 inches.
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 inches. The height is given as 4 inches.
Area = 1/2 * 6 in * 4 in = 12 in²
So the area of one triangular face is 12 in².
The area of the base is given by the formula for the area of a square:
Area = side * side = 6 in * 6 in = 36 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 (A) 72 in².