Leigh Ann is designing a wrapper for a new dark chocolate candy bar that her company is going to sell. The candy bar is a triangular prism. The dimensions of the candy bar are shown in the diagram.
6.9 cm, 7.4 cm, 5.1 cm, 9.9 cm, 7.4 cm
Which measurement is closest to the total surface area of the candy bar in square centimeters?
a 232.20 cm^2
b 197.01 cm^2
c 265.32 cm^2
d 174.19 cm^2
To calculate the total surface area of the triangular prism, we need to find the area of each face and add them together.
The triangular faces have the dimensions 6.9 cm, 5.1 cm, and 7.4 cm. We can use Heron's formula to find the area of each triangle:
s = (6.9 + 5.1 + 7.4) / 2
s = 19.4 / 2
s = 9.7
Area of triangular face = √(9.7 * (9.7 - 6.9) * (9.7 - 5.1) * (9.7 - 7.4))
Area of triangular face = √(9.7 * 2.8 * 4.6 * 2.3)
Area of triangular face ≈ √(223.8408)
Area of triangular face ≈ 14.96 cm^2
There are two triangular faces, so the total area of the triangular faces is 14.96 cm^2 * 2 = 29.92 cm^2.
The rectangular face has the dimensions 7.4 cm by 9.9 cm. The area of the rectangular face is 7.4 cm * 9.9 cm = 73.26 cm^2.
The total surface area is the sum of the triangular faces and the rectangular face, so:
Total surface area = 29.92 cm^2 + 73.26 cm^2
Total surface area ≈ 103.18 cm^2
The measurement that is closest to the total surface area of the candy bar in square centimeters is 103.18 cm^2, which is not one of the given options. Therefore, none of the options a, b, c, or d are correct.