Answer:
The surface area of the square pyramid is approximately 864.2 square centimeters.
Explanation:
To solve for the surface area of a square pyramid, you need to find the area of the base and the area of each of the four triangular faces.
The area of the base is simply the square of the length of one side. So, for a base with edge lengths of 15 centimeters, the area of the base is:
15^2 = 225 square centimeters.
To find the area of each of the four triangular faces, you need to use the formula:
(area of triangle) = 1/2 x (base of triangle) x (height of triangle)
For a square pyramid, the height of each triangular face is equal to the slant height of the pyramid, which can be found using the Pythagorean theorem:
(hypotenuse)^2 = (height)^2 + (1/2 x base)^2
In this case, the height is given as 20 centimeters and the base is half of the base edge of the pyramid, or 7.5 centimeters. So, the slant height is:
hypotenuse = sqrt(20^2 + 7.5^2) = 21.3 centimeters
Now you can use this slant height to find the area of each triangular face:
(area of triangle) = 1/2 x (base of triangle) x (height of triangle)
= 1/2 x (15) x (21.3)
= 159.8 square centimeters
So, the total surface area of the square pyramid is:
225 (area of base) + 4 x 159.8 (area of each triangular face)
= 225 + 639.2
= 864.2 square centimeters.
Therefore, the surface area of the square pyramid is approximately 864.2 square centimeters.