A square pyramid has a square base and four triangular faces. To find the surface area, we need to find the area of the base and the combined areas of the four triangular faces.
The area of the base can be found by squaring the length of one side of the square base:
Area of base = (side length)^2
Area of base = (10 cm)^2
Area of base = 100 cm^2
To find the area of one triangular face, we can use the formula:
Area of triangle = (base length * height) / 2
In this case, the base length is the same as the side length of the square base, which is 10 cm. The height of the triangular face can be found using the Pythagorean theorem:
height = sqrt((slant height)^2 - (base length / 2)^2)
height = sqrt((20 cm)^2 - (10 cm / 2)^2)
height = sqrt(400 cm^2 - 25 cm^2)
height = sqrt(375 cm^2)
height ≈ 19.36 cm
Area of one triangular face = (10 cm * 19.36 cm) / 2
Area of one triangular face ≈ 96.80 cm^2
Since there are four triangular faces, the combined area of the triangular faces is:
Combined area of triangular faces = 4 * 96.80 cm^2
Combined area of triangular faces ≈ 387.20 cm^2
Finally, to find the surface area of the square pyramid, we add the area of the base to the combined area of the triangular faces:
Surface area = Area of base + Combined area of triangular faces
Surface area = 100 cm^2 + 387.20 cm^2
Surface area ≈ 487.20 cm^2
Therefore, the surface area of the square pyramid is approximately 487.20 square cm.
What is the surface area of a square pyramid with base length of 10 cm and slant height of 20 cm
1 answer
1 answer