The two-dimensional net shows three rectangles one above the other. The length of the rectangles is 8 inches. The bottom rectangle has one right triangle on its right and one right... The two-dimensional net shows three rectangles one above the other. The length of the rectangles is 8 inches. The bottom rectangle has one right triangle on its right and one right triangle on its left. The width of the bottom rectangle and the height of the rectangle is 4 inches. The base of the right triangle is 3 inches and the slant height is 5 inches.
Understand the Problem
The question describes a two-dimensional net composed of three rectangles and two right triangles. The task would likely involve calculating the surface area or volume of the three-dimensional shape formed when the net is folded. We need to use the given dimensions of the rectangles and triangles to determine the required measurements such as surface area.
Answer
156 square inches
Answer for screen readers
156 square inches
Steps to Solve
- Identify the 3D shape
The two-dimensional net described, when folded, forms a triangular prism. 2. Calculate the area of the three rectangles
The prism has three rectangular faces. Two rectangles have dimensions 8 inches by 4 inches. The third rectangle has dimensions 8 inches by 3 inches + 3 inches (base of each rectangle is 3 inches) + 4 inches (width of rectangle); therefore 8 inches by 10 inches.
Area of the two identical rectangles $A_1 = 8 \times 4 = 32 \text{ square inches}$ Total area for both rectangles: $2 \times 32 = 64 \text{ square inches}$
Area of the larger rectangle $A_2 = 8 \times 10 = 80 \text{ square inches}$ 3. Calculate the area of the two triangles
The prism has two triangular faces. The area of a triangle is given by one-half times base times height. The base of each right triangle is 3 inches, and the height is 4 inches.
Area of one triangle $A_3 = \frac{1}{2} \times 3 \times 4 = 6 \text{ square inches}$ Total area for both triangles: $2 \times 6 = 12 \text{ square inches}$ 4. Calculate the total surface area
The total surface area of the triangular prism is the sum of the areas of the three rectangles and the two triangles.
$A_{total} = A_1 + A_2 + A_3 = 64 + 80 + 12 = 156 \text{ square inches}$
156 square inches
More Information
The surface area calculation includes all faces of the triangular prism: two triangular faces and three rectangular faces.
Tips
A common mistake is to forget one of the faces when calculating the surface area, or to incorrectly calculate the area of one of the rectangles or triangles. Be sure to double check each calculation and account for all faces.
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