Calculate the surface area of the three-dimensional figure represented in the net shown. All measurements are in centimeters.HINT: The formula for the area of a rectangle is 𝐴=𝑙×𝑤. The formula for the area of a triangle is 𝐴=𝑏×ℎ2.View Image DescriptionA net is drawn on a coordinate plane with the following attributes:It is composed of 4 triangles and one rectangle.The rectangle is labeled ABCD.The vertices of the rectangle are plotted at A (0,0), B (10,0), C (10, 4), D (0,4).The triangles formed by side DC and AB have a height of 6.32 labeled.The triangles formed by AD and BC have a height of 7.81 labeled.40 square centimeters268.98 square centimeters80 square centimeters134.44 square centimeters
Question
Calculate the surface area of the three-dimensional figure represented in the net shown. All measurements are in centimeters.HINT: The formula for the area of a rectangle is 𝐴=𝑙×𝑤. The formula for the area of a triangle is 𝐴=𝑏×ℎ2.View Image DescriptionA net is drawn on a coordinate plane with the following attributes:It is composed of 4 triangles and one rectangle.The rectangle is labeled ABCD.The vertices of the rectangle are plotted at A (0,0), B (10,0), C (10, 4), D (0,4).The triangles formed by side DC and AB have a height of 6.32 labeled.The triangles formed by AD and BC have a height of 7.81 labeled.40 square centimeters268.98 square centimeters80 square centimeters134.44 square centimeters
Solution
To calculate the surface area of the three-dimensional figure, we need to calculate the area of each shape in the net and then add them together.
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Calculate the area of the rectangle ABCD: The length (l) is 10 cm and the width (w) is 4 cm. Using the formula for the area of a rectangle (A = l * w), we get: A = 10 cm * 4 cm = 40 square cm.
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Calculate the area of the two triangles formed by sides DC and AB: The base (b) is 4 cm (the same as the width of the rectangle) and the height (h) is 6.32 cm. Using the formula for the area of a triangle (A = 0.5 * b * h), we get: A = 0.5 * 4 cm * 6.32 cm = 12.64 square cm. Since there are two such triangles, the total area is 2 * 12.64 square cm = 25.28 square cm.
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Calculate the area of the two triangles formed by sides AD and BC: The base (b) is 10 cm (the same as the length of the rectangle) and the height (h) is 7.81 cm. Using the formula for the area of a triangle (A = 0.5 * b * h), we get: A = 0.5 * 10 cm * 7.81 cm = 39.05 square cm. Since there are two such triangles, the total area is 2 * 39.05 square cm = 78.1 square cm.
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Add up the areas of all the shapes to get the total surface area of the three-dimensional figure: Total surface area = 40 square cm (rectangle) + 25.28 square cm (two triangles DC and AB) + 78.1 square cm (two triangles AD and BC) = 143.38 square cm.
So, the surface area of the three-dimensional figure is 143.38 square centimeters.
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