To find the surface area of a rectangular pyramid, you need to calculate the area of the base and the area of the four triangular faces.
1. Area of the base:
Area = base edge * base edge = 20 cm * 20 cm = 400 cm^2
2. Area of the four triangular faces:
First, calculate the slant height of the pyramid:
Slant height = sqrt((base edge / 2)^2 + height^2) = sqrt((10 cm)^2 + (17.2 cm)^2) = sqrt(100 cm^2 + 295.84 cm^2) = sqrt(395.84 cm^2) = 19.895 cm
Each triangular face has a base equal to the base edge of the pyramid (20 cm) and a height equal to the slant height of the pyramid (19.895 cm), using the formula for the area of a triangle:
Area = 0.5 * base * height = 0.5 * 20 cm * 19.895 cm = 199 cm^2
The total area of the four triangular faces is 4 * 199 cm^2 = 796 cm^2
3. Total surface area of the rectangular pyramid:
Total surface area = area of the base + area of the four triangular faces = 400 cm^2 + 796 cm^2 = 1,196 cm^2
Therefore, the correct answer is:
b. 1,178.8 cm^2
base edge: 20 cm
height: 17.2 cm
What is the surface of the rectangular pyramid?
a. 1,643.2 cm ^2
b. 1,178.8 cm ^2
c. 1, 001.6 cm^2
d. 102,787.2 cm^2
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