Find the surface area of the regular pyramid shown to the nearest whole number. The figure is not drawn to scale. (1 point) Responses 1,540 m2 1,540 m 2 770 m2 770 m 2 396 m2 396 m 2 749 m2
To find the surface area of a regular pyramid, you need to calculate the area of the base and the lateral faces separately.
Given that the base is a square with side length 15 m, the area of the base is:
Area of base = side length^2 = 15^2 = 225 m^2
To calculate the lateral faces, we first need to find the slant height (l).
Using the Pythagorean theorem, l^2 = 15^2 + 12^2
l^2 = 225 + 144
l^2 = 369
l = √369
l ≈ 19.2 m
The lateral faces include 4 triangular faces with base 15 m and height 19.2 m:
Area of 1 triangular face = 0.5 * base * height = 0.5 * 15 * 19.2 ≈ 144 m^2
Since there are 4 triangular faces, the total lateral face area = 4 * 144 ≈ 576 m^2
Therefore, the total surface area of the pyramid is:
225 (area of base) + 576 (lateral face area) = 801 m^2
Rounded to the nearest whole number, the surface area of the regular pyramid is 801 m^2.
Therefore, none of the given responses match the calculated surface area.