Use the image to answer the question.
An illustration shows a triangular prism. The front triangular face is visible. The right rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. The left side of the triangle measures 10 centimeters. The right side of the triangle also measures 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 6 centimeters. The base of the triangle measures 8 centimeters.
What is the missing length l
of the triangular prism if the surface area is 524 square centimeters?
(1 point)
Responses
10 cm
10 cm
8 cm
8 cm
17 cm
17 cm
16 cm
16 cm
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The missing length of the triangular prism can be found using the formula for the surface area of a prism, which is given by:
Surface Area = 2(base area) + (perimeter of base) * height
In this case, the base area is the area of the front triangular face, which is (1/2) * base * height. The perimeter of the base is the sum of all three sides, which is 10 cm + 8 cm + l. The height of the prism is 6 cm.
Given that the surface area is 524 square centimeters, the equation can be set up as:
524 = 2((1/2) * 8 * 6) + (10 + 8 + l) * 6
524 = 48 + (18 + l) * 6
524 = 48 + 108 + 6l
524 = 156 + 6l
368 = 6l
l = 61.33 cm
Therefore, the missing length of the triangular prism is approximately 61.33 cm.