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
16 cm
16 cm
17 cm
17 cm
10 cm
10 cm
Skip to navigation
To find the missing length, we first need to calculate the lateral surface area of the triangular prism.
The lateral surface area of a triangular prism is given by the formula:
Lateral Surface Area = perimeter of the base x height of the prism
In this case, the perimeter of the base is the sum of the three sides of the triangle, which is 10 + 10 + 8 = 28 cm.
So, the lateral surface area is:
28 cm x 6 cm = 168 square cm
The total surface area of the triangular prism is the sum of the lateral surface area and the areas of the two triangular faces.
Since we are given that the total surface area is 524 square cm, we can calculate the areas of the two triangular faces:
Area of one triangular face = (1/2) x base x height = (1/2) x 8 cm x 6 cm = 24 square cm
Total area of both triangular faces = 2 x 24 square cm = 48 square cm
Now, subtract the total surface area by the area of both triangular faces to find the lateral surface area:
524 square cm - 48 square cm = 476 square cm
Set the lateral surface area equal to the perimeter of the base x height of the prism, and solve for the missing length l:
476 square cm = 28 cm x l
l = 476 square cm / 28 cm
l ≈ 17 cm
Therefore, the missing length l of the triangular prism is 17 cm.
Correct answer: 17 cm