Surface Area of Triangular Prisms Quick Check
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Question
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
16 cm
16 cm
17 cm
17 cm
My apologies for the mistake. Let's calculate the missing length \(l\):
The surface area of a triangular prism is given by the formula:
Surface Area = 2(Base Area) + (perimeter of base x height).
Given:
Base of the triangle = 8 cm
Height of the triangle = 6 cm
The base area of the triangle:
Base Area = (1/2) x base x height
Base Area = (1/2) x 8 cm x 6 cm
Base Area = 24 square cm
The perimeter of the base of the triangle:
Perimeter = 8 cm + 10 cm + 10 cm = 28 cm
The missing length represents the length of the rectangular face:
Surface Area = 2(24 square cm) + (28 cm x l)
524 = 48 + 28l
476 = 28l
l = 17 cm
Therefore, the missing length of the triangular prism is 17 cm.