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How to Find Surface Area of a Triangular Prism Using a Net | Side Lengths & Area Calculation
Mathematics
Grade 7 (Junior High School)
Question Content
Using a net to find the surface area of a triangular prism. (a) Find the following side lengths for the net: A = __ ft, B = __ ft, C = __ ft, D = __ ft. (b) Use the net to find the surface area of the prism. __ ft². The triangular prism has triangular bases with side lengths 6 ft, 8 ft, 10 ft, and the height of the triangular base is 4 ft.
Correct Answer
(a) A=10 ft, B=4 ft, C=6 ft, D=8 ft; (b) 168 ft²
Detailed Solution Steps
1
Step 1: Identify side lengths for the net (part a):
2
- A corresponds to the longest side of the triangular base, so A = 10 ft.
3
- B corresponds to the height of the triangular base, so B = 4 ft.
4
- C corresponds to one of the shorter sides of the triangular base, so C = 6 ft.
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- D corresponds to the remaining side of the triangular base, so D = 8 ft.
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Step 2: Calculate the surface area (part b):
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- First, find the area of the two triangular bases: Area of one triangle = (1/2)*base*height = (1/2)*8*4 = 16 ft². Total area for two triangles = 2*16 = 32 ft².
8
- Next, find the area of the three rectangular faces: Face 1 (8 ft side): 8*10 = 80 ft²; Face 2 (6 ft side): 6*10 = 60 ft²; Face 3 (10 ft side): 10*10 = 100 ft². Total area for rectangles = 80 + 60 + 100 = 136 ft².
9
- Add the area of the triangular bases and rectangular faces to get total surface area: 32 + 136 = 168 ft².
Knowledge Points Involved
1
Net of a Triangular Prism
A net is a 2D unfolded representation of a 3D shape. For a triangular prism, the net consists of two congruent triangular bases and three rectangular faces connected to each side of the triangles. It is used to visualize and calculate surface area by summing the area of all individual faces.
2
Area of a Triangle
The formula for the area of a triangle is (1/2)*base*height, where the height is the perpendicular distance from the base to the opposite vertex. This is used to find the area of the triangular bases of the prism.
3
Area of a Rectangle
The formula for the area of a rectangle is length*width. For a triangular prism, the length of each rectangle is the length of the prism, and the width is the length of one side of the triangular base.
4
Surface Area of a Triangular Prism
The total surface area is the sum of the areas of all faces of the prism. It can be calculated using the net by adding the area of the two triangular bases and the area of the three rectangular lateral faces.
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