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
17 cm
17 cm
16 cm
16 cm
10 cm
10 cm
8 cm
8 cm
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The surface area of a triangular prism can be found using the formula:
Surface Area = 2(Base area) + (perimeter of base x height)
In this case, the base area is the area of the triangular face, which can be found using the formula for the area of a triangle:
Base area = (1/2) x base x height
Base area = (1/2) x 8 cm x 6 cm = 24 square cm
The perimeter of the base = 8 cm + 10 cm + 10 cm = 28 cm
Plugging these values into the surface area formula, we get:
524 square cm = 2(24) + 28l
524 = 48 + 28l
476 = 28l
l = 17 cm
Therefore, the missing length l of the triangular prism is 17 cm.