To find the surface area of a triangular prism, you need to calculate the sum of the areas of all its faces.
In this case, the front triangular face has an area of (1/2) x base x height = (1/2) x 8 x 6 = 24 square centimeters.
The right rectangular face has an area of length x width = x x 10 = 80 square centimeters.
Since the surface area is 524 square centimeters, the missing length (l) can be calculated as follows:
524 = 2(24) + 80 + 10l
524 = 48 + 80 + 10l
524 = 128 + 10l
396 = 10l
l = 39.6 cm
Therefore, the missing length is 39.6 cm, which is closest to the option 40 cm.
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
16 cm
16 cm
10 cm
10 cm
17 cm
17 cm
8 cm
8 cm
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1 answer