To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces.
1. Area of the base:
The base of the pyramid is a square with side length of 12. The area of a square is calculated by squaring the side length:
Base Area = 12 * 12 = 144
2. Area of the triangular faces:
Since the pyramid has a square base, the triangular faces are isosceles triangles with base length of 12 and height equal to the slant height (18). The formula to calculate the area of a triangle is:
Area = 1/2 * base * height
Each triangular face area = 1/2 * 12 * 18 = 108
Since there are 4 triangular faces, the total area of the triangular faces = 4 * 108 = 432
3. Total surface area:
The total surface area of the pyramid is the sum of the base area and the areas of the four triangular faces:
Surface Area = Base Area + Triangular Faces Area = 144 + 432 = 576
Therefore, the surface area of the square pyramid is 576.
Calculate the surface area of the quare pyramid that has a base length of 12 and a slant height of 18. Show your work.
1 answer
1 answer