First, since it is a square pyramid, we know that the base is a square. Therefore, the base of the pyramid is 15ft by 15ft.
To find the surface area of the square pyramid, we need to find the area of the base and the area of the four triangular faces.
Area of the base = side of the square x side of the square
Area of the base = 15ft x 15ft
Area of the base = 225 square feet
Next, we need to find the area of each triangular face. Since the base of the pyramid is a square, the triangles are isosceles triangles, and one leg is the height of the pyramid and the other leg is half of one side of the square base.
The height of the pyramid is given as 9.9ft, so the length of the other leg of the triangle is half of one side of the square base which is 15ft / 2 = 7.5ft.
Area of each triangular face = 0.5 x base x height
Area of each triangular face = 0.5 x 7.5ft x 9.9ft
Area of each triangular face = 0.5 x 74.25 square feet
Area of each triangular face = 37.125 square feet
There are a total of 4 triangular faces in the pyramid, so the total area of the four triangular faces = 4 x 37.125 square feet = 148.5 square feet
Therefore, the total surface area of the square pyramid = area of the base + area of four triangular faces
Total surface area = 225 square feet + 148.5 square feet
Total surface area = 373.5 square feet
Therefore, the surface area of the square pyramid is 373.5 square feet.
Solve the surface area of the square pyramid 15ft 9.9ft
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