Unit six surface area lesson seven surface area pyramids quick check answers
1. A pyramid has a square base with sides of length 8 cm. The slant height of the pyramid is 10 cm. What is the surface area of the pyramid?
To find the surface area of a pyramid, we need to calculate the area of the base and the area of the four triangular faces.
Area of base = side length^2
Area of base = 8 cm^2 = 64 cm^2
Area of each triangular face = 0.5 * base * height
Area of each triangular face = 0.5 * 8 cm * 10 cm = 40 cm^2
Total surface area = base area + 4 triangular faces area
Total surface area = 64 cm^2 + 4 * 40 cm^2 = 224 cm^2
The surface area of the pyramid is 224 cm^2.
2. A pyramid has a triangular base with a base length of 6 cm and a height of 8 cm. The slant height of the pyramid is 10 cm. What is the surface area of the pyramid?
Area of base = 0.5 * base * height
Area of base = 0.5 * 6 cm * 8 cm = 24 cm^2
Area of each triangular face = 0.5 * base * height
Area of each triangular face = 0.5 * 6 cm * 10 cm = 30 cm^2
Total surface area = base area + 3 triangular faces area
Total surface area = 24 cm^2 + 3 * 30 cm^2 = 114 cm^2
The surface area of the pyramid is 114 cm^2.