Solve for the surface area for the square pyramid on the front bottom is 15 feet and on the right side they have a line going down the middle and it says 9.9 feet. What would the answer be
To solve for the surface area of the square pyramid, you need to find the areas of each of the four triangular faces and the square base, and then add them together.
Given:
Front bottom side of the square pyramid = 15 feet
Line going down the middle on the right side = 9.9 feet
First, find the length of each side of the base square. Since it is a square, all sides are equal in length.
Let's call each side of the square base "s".
From the information given:
s = 15 feet
Next, find the slant height of the triangular faces using the Pythagorean theorem, where one leg is half of the side of the base square and the hypotenuse is the given length of the line going down the middle on the right side.
Let's call the slant height "l":
l^2 = (s/2)^2 + (9.9)^2
l^2 = (15/2)^2 + (9.9)^2
l^2 = 7.5^2 + 9.9^2
l^2 = 56.25 + 98.01
l^2 = 154.26
l ≈ √154.26
l ≈ 12.42 feet
Now, calculate the surface area of the square pyramid.
Area of square base = s^2
Area of square base = 15^2
Area of square base = 225 square feet
Area of each triangular face = (1/2) * base * height
Area of each triangular face = (1/2) * 15 * 12.42
Area of each triangular face = 93.15 square feet
Total surface area = 4 * (area of triangular face) + (area of square base)
Total surface area = 4 * 93.15 + 225
Total surface area = 372.6 + 225
Total surface area ≈ 597.6 square feet
Therefore, the surface area of the square pyramid is approximately 597.6 square feet.