Answer: The composite figure consists of two square pyramids, so we can find the total surface area by adding the surface area of each pyramid. The surface area of a square pyramid is given by:
S = B + (1/2)Pl
where B is the area of the base, P is the perimeter of the base, l is the slant height, and S is the total surface area.
For each pyramid, we have:
B = 24^2 = 576 cm^2
P = 4(24) = 96 cm
l = sqrt(24^2 + 5^2) = 25 cm
So the surface area of each pyramid is:
S = 576 + (1/2)(96)(25)
S = 576 + 1200
S = 1776 cm^2
Therefore, the total surface area of the composite figure is:
2S = 2(1776)
= 3532 cm^2
The expression that represents the total surface area, in square centimeters, of the figure is:
(24) (24) + 8 (one-half (24) (5)) + 8 (one-half (24) (13)) = 576 + 480 + 624 = 1680 cm^2
This expression only accounts for the surface area of the base and the triangular faces, but it does not include the surface area of the pyramid faces. So it is not correct.
The correct answer is:
8 (one-half (24) (5)) + 8 (one-half (24) (13)) = 480 + 624 = 1104 cm^2
which only represents the surface area of the triangular faces of both pyramids. To get the total surface area, we need to add the surface area of the base, which gives:
1104 + 2(576) = 2256 + 1104 = 3360 cm^2
Therefore, the total surface area of the composite figure is 3360 square centimeters.
Explanation: