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
17 cm
17 cm
16 cm
16 cm
8 cm
8 cm
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To find the missing length l of the triangular prism, we first need to calculate the surface area of the prism.
Surface Area = 2(Base Area) + (Perimeter of Base) * Height
The base area of the triangle is (1/2) * base * height = (1/2) * 8 * 6 = 24 square centimeters.
The perimeter of the base is 8 + 10 + 10 = 28 centimeters.
Therefore, the surface area = 2(24) + 28 * l = 48 + 28l.
Given that the surface area is 524 square centimeters, we can set up the equation:
48 + 28l = 524
28l = 476
l = 17 cm
Therefore, the missing length of the triangular prism is 17 cm.