An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 9 centimeters. The perpendicular side of the triangular face measures 5 centimeters and the hypotenuse measures 13 centimeters.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
(1 point)
Responses
330 cm2
330 cm squared
287 cm2
287 cm squared
810 cm2
810 cm squared
240 cm2
240 cm squared
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To find the total surface area of the triangular prism (wedge of cheese), we need to calculate the area of all six faces.
1. The area of the triangular face (base) can be calculated using the formula for the area of a triangle: 1/2 * base * perpendicular height
Area = 1/2 * 9 * 5 = 22.5 cm2
2. Since there are two triangular faces on the prism, we need to multiply the area by 2: 22.5 * 2 = 45 cm2
3. The area of the three rectangular faces can be calculated using the formula for the surface area of a rectangular prism: 2 * (length * width + height * width)
Area = 2 * (12 * 9 + 9 * 5) = 2 * (108 + 45) = 2 * 153 = 306 cm2
4. Therefore, the total surface area of the triangular prism (wedge of cheese) is the sum of the areas of the triangular faces and the rectangular faces: 45 + 306 = 351 cm2
Therefore, the answer is not listed in the options provided. It should be 351 cm2.