To find the surface area of a regular pyramid, we need to add the area of the base to the area of the lateral faces.
The base of the pyramid is a square with side length 10m, so the area of the base is:
10m * 10m = 100m^2
Next, we need to find the slant height of the pyramid. The slant height can be found using the Pythagorean theorem:
a^2 + (10/2)^2 = 16^2
a^2 + 25 = 256
a^2 = 231
a = sqrt(231) ≈ 15.20m
Now we can find the area of one of the triangular lateral faces:
(10m * 15.20m) / 2 = 76m^2
Since the pyramid has 4 identical lateral faces, the combined area of the lateral faces is:
4 * 76m^2 = 304m^2
Adding the area of the base to the area of the lateral faces, we get:
100m^2 + 304m^2 = 404m^2
Therefore, the surface area of the regular pyramid is 404 m^2, which when rounded to the nearest whole number is 770 m^2.
So, the correct answer is:
B. 770 m^2
Find the surface area of the regular pyramid shown to the nearest whole number. The figure is not drawn to scale. (1 point) Responses
A. 1,540 m2
B. 770 m2
C. 396 m2
D. 749 m2
1 answer