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
17 cm
17 cm
10 cm
10 cm
8 cm
To find the missing length l of the triangular prism, we first need to calculate the lateral surface area of the triangular prism.
The lateral surface area of a triangular prism can be calculated using the formula:
Lateral Surface Area = perimeter of the base x height
The perimeter of the base can be found by adding the three sides of the triangle:
Perimeter of base = 10 cm + 10 cm + 8 cm = 28 cm
Now, substitute the values into the formula:
Lateral Surface Area = 28 cm x 6 cm = 168 square cm
The total surface area of the triangular prism is given as 524 square cm. So, we subtract the lateral surface area from the total surface area to find the surface area of the two triangular faces:
Surface area of two triangular faces = 524 square cm - 168 square cm = 356 square cm
Since there are two triangular faces, each face has an area of 178 square cm.
Using the formula for the area of a triangle A = 1/2 x base x height, we can calculate the missing length l:
178 square cm = 1/2 x 8 cm x l
178 = 4l
l = 178/4 = 44.5 cm
Therefore, the missing length l of the triangular prism is approximately 44.5 cm.