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
8 cm
8 cm
16 cm
16 cm
10 cm
10 cm
17 cm
17 cm
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The missing length l of the triangular prism can be calculated using the surface area formula for a triangular prism:
Surface Area = 2(Base area) + (Perimeter of base)*(Height)
Given:
Base area = 1/2 * base * height = 1/2 * 8 * 6 = 24 sq cm
Perimeter of base = 10 + 10 + 8 = 28 cm
Height = 6 cm
Plugging in the values:
524 = 2(24) + 28*l
524 = 48 + 28l
476 = 28l
l = 17
Therefore, the missing length l of the triangular prism is 17 cm.