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
To find the surface area of the triangular prism, we need to calculate the areas of the three rectangular faces and the two triangular faces.
The formula for the surface area of a triangular prism is:
Surface area = (2 * base area) + (base perimeter * height)
The base area is equal to the area of a triangle, which can be calculated using the formula:
Area = (base * height) / 2
Given the dimensions of the candy bar:
Base 1 = 6.9 cm
Base 2 = 7.4 cm
Height = 5.1 cm
Base 3 = 9.9 cm
Base 4 = 7.4 cm
First, let's calculate the area of the triangular faces:
Triangle 1 area = (6.9 * 5.1) / 2 = 17.595 cm^2
Triangle 2 area = (9.9 * 5.1) / 2 = 25.245 cm^2
Next, let's calculate the base area:
Base 1 area = 6.9 * 5.1 = 35.19 cm^2
Base 2 area = 7.4 * 5.1 = 37.74 cm^2
Base 3 area = 9.9 * 7.4 = 73.26 cm^2
Now, let's calculate the base perimeter:
Base 1 perimeter = 2 * (6.9 + 5.1) = 24 cm
Base 2 perimeter = 2 * (7.4 + 5.1) = 24.2 cm
Finally, let's calculate the total surface area:
Surface area = (2 * base area) + (base perimeter * height)
Surface area = (2 * (35.19 + 37.74 + 73.26)) + (24 + 24.2) * 5.1
Surface area = (2 * 146.19) + (48.2) * 5.1
Surface area = 292.38 + 245.82
Surface area = 538.20 cm^2
The measurement closest to the total surface area of the candy bar is 538.20 cm^2.
Therefore, the correct answer is not given in the options provided.