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
8 cm
16 cm
17 cm
The missing length l can be calculated by finding the area of the triangular face and the area of the rectangular face, then adding them up.
The area of the front triangular face is (1/2) x base x height = (1/2) x 8 cm x 6 cm = 24 square cm.
The area of the right rectangular face is length x width = l x 10 cm.
The total surface area is given as 524 square cm.
So, 24 + 10l = 524.
10l = 500.
l = 50 cm / 10 = 5 cm.
Therefore, the missing length l of the triangular prism is 5 cm.
wrtong
Apologies for the error in the previous response. Let's correct it:
The total surface area of the triangular prism can be calculated by finding the areas of all the faces and adding them together.
1. The area of the front triangular face is (1/2) x base x height = (1/2) x 8 cm x 6 cm = 24 square cm.
2. The area of the rear triangular face will be the same as the front triangular face, 24 square cm.
3. The area of the right rectangular face is length x height = l x 6 cm.
4. The area of the left rectangular face will also be l x 6 cm.
5. The area of the top rectangular face is 10 cm x 8 cm = 80 square cm.
6. The area of the bottom rectangular face is the same as the top, 80 square cm.
Adding all these areas together, we get the total surface area = 24 + 24 + 2l(6) + 2(10 x 8) = 524 square cm.
Solving for l:
48 + 12l + 160 = 524
12l + 208 = 524
12l = 316
l = 316 / 12 = 26.33 cm
Therefore, the missing length l of the triangular prism is approximately 26.33 cm.
wrong
I apologize for the errors in the previous calculations. Let's correct it again:
The total surface area of the triangular prism can be calculated using the following formula:
Total Surface Area = 2(base area of the triangular faces) + (sum of all rectangular faces)
Area of the triangular faces (front and back):
Area = (1/2) x base x height
Area = (1/2) x 8 cm x 6 cm
Area = 24 square cm
Sum of all rectangular faces:
Height of the rectangular faces = 6 cm
Area = 2(l x 6) + 2(10 x 8)
Area = 12l + 160
Given Total Surface Area = 524 square cm
Therefore,
2(24) + 12l + 160 = 524
48 + 12l + 160 = 524
12l + 208 = 524
12l = 316
l = 316 / 12
l = 26.33 cm
Therefore, the missing length (l) of the triangular prism is approximately 26.33 cm.