Calculate the surface area of the 3D shape formed by the described two-dimensional net.
Understand the Problem
The question describes a two-dimensional net composed of three rectangles and two right triangles. The task is likely to calculate the surface area or volume of a three-dimensional shape that can be formed by folding this net. To do this, we will need to use the dimensions provided to calculate the areas of each rectangle and triangle, and then sum these areas to find the total surface area. The rectangle has dimensions 8 inches by 4 inches, and the right triangles have a base of 3 inches, a height of 4 inches, and a hypotenuse of 5 inches.
Answer
The total area of the net is $108$ square inches.
Answer for screen readers
The total area of the net is 108 square inches.
Steps to Solve
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Calculate the area of one rectangle
The area of a rectangle is given by the formula: Area = length × width. In this case, the length is 8 inches and the width is 4 inches. So, the area of one rectangle is: $Area = 8 \times 4 = 32$ square inches.
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Calculate the total area of the three rectangles
Since there are three identical rectangles, the total area of the rectangles is: $3 \times 32 = 96$ square inches.
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Calculate the area of one right triangle
The area of a right triangle is given by the formula: Area = $\frac{1}{2}$ × base × height. In this case, the base is 3 inches and the height is 4 inches. So, the area of one right triangle is: $Area = \frac{1}{2} \times 3 \times 4 = 6$ square inches.
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Calculate the total area of the two right triangles
Since there are two identical right triangles, the total area of the triangles is: $2 \times 6 = 12$ square inches.
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Calculate the total area of the net
The total area of the net is the sum of the areas of the three rectangles and the two right triangles. $Total\ Area = 96 + 12 = 108$ square inches.
The total area of the net is 108 square inches.
More Information
The given two-dimensional net can be folded to form a triangular prism. The three rectangles form the lateral faces of the prism, and the two right triangles form the bases of the prism. The surface area of the net is equal to the surface area of the triangular prism.
Tips
A common mistake is to forget to multiply the area of a single rectangle or triangle by the number of rectangles or triangles present in the net. Another mistake is to use the slant height (hypotenuse) of the triangle in the area calculation instead of the actual height. It is also important to carefully identify the base and height of the triangles.
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