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
17 cm
17 cm
16 cm
16 cm
10 cm
10 cm
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To find the missing length, we first need to calculate the total surface area of the triangular prism.
The total surface area of a triangular prism can be calculated using the formula:
Total Surface Area = 2*(base area of triangle) + (perimeter of triangle)*(l)
Given measurements:
- Base of the triangle = 8 cm
- Left side of triangle = 10 cm
- Right side of triangle = 10 cm
- Perpendicular height = 6 cm
- Total surface area = 524 sq. cm
First, calculate the base area of the triangle:
Base area = (1/2)*(base)*(height) = (1/2)*(8 cm)*(6 cm) = 24 sq. cm
Now, calculate the perimeter of the triangle:
Perimeter = Left side + Right side + Base = 10 cm + 10 cm + 8 cm = 28 cm
Plug the values into the formula for total surface area:
524 sq. cm = 2*(24 sq. cm) + (28 cm)*(l)
524 sq. cm = 48 sq. cm + 28 cm*l
476 sq. cm = 28 cm*l
l = 476 sq. cm / 28 cm
l = 17 cm
Therefore, the missing length of the triangular prism is 17 cm.
The correct answer is:
17 cm