Question
What is the total surface area represented by this net of a triangular prism that is 9cm, 17cm, 7.8 cm, 17cm, 9, 17cm and 9cm
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Answered by
GPT 3.5
To find the total surface area of the triangular prism, we need to calculate the areas of each of the surfaces:
1. Base triangles: The base of the triangular prism is an isosceles triangle with side lengths of 9 cm, 17 cm, and 17 cm. We can calculate the area of one base triangle using the formula for the area of a triangle: (1/2) * base * height. In this case, the base is 9 cm and the height can be calculated using the Pythagorean theorem:
height = sqrt(17^2 - (9/2)^2) = √(289 - 40.5) = √248.5 ≈ 15.77 cm
Area of one base triangle = (1/2) * 9 * 15.77 ≈ 70.97 cm^2
Since there are two base triangles, the total area of the base is 2 * 70.97 = 141.94 cm^2.
2. Rectangular faces: There are three rectangular faces on a triangular prism. Two of the faces are rectangles with dimensions 9 cm by 17 cm, and the third face is a rectangle with dimensions 17 cm by 7.8 cm.
Area of the first two rectangles = 2 * 9 * 17 = 306 cm^2
Area of the third rectangle = 17 * 7.8 = 132.6 cm^2
Total area of the rectangular faces = 306 + 132.6 = 438.6 cm^2
Adding the areas of the base triangles and rectangular faces together, we get the total surface area of the triangular prism:
Total surface area = 141.94 + 438.6 = 580.54 cm^2
Therefore, the total surface area represented by this net of a triangular prism is approximately 580.54 cm^2.
1. Base triangles: The base of the triangular prism is an isosceles triangle with side lengths of 9 cm, 17 cm, and 17 cm. We can calculate the area of one base triangle using the formula for the area of a triangle: (1/2) * base * height. In this case, the base is 9 cm and the height can be calculated using the Pythagorean theorem:
height = sqrt(17^2 - (9/2)^2) = √(289 - 40.5) = √248.5 ≈ 15.77 cm
Area of one base triangle = (1/2) * 9 * 15.77 ≈ 70.97 cm^2
Since there are two base triangles, the total area of the base is 2 * 70.97 = 141.94 cm^2.
2. Rectangular faces: There are three rectangular faces on a triangular prism. Two of the faces are rectangles with dimensions 9 cm by 17 cm, and the third face is a rectangle with dimensions 17 cm by 7.8 cm.
Area of the first two rectangles = 2 * 9 * 17 = 306 cm^2
Area of the third rectangle = 17 * 7.8 = 132.6 cm^2
Total area of the rectangular faces = 306 + 132.6 = 438.6 cm^2
Adding the areas of the base triangles and rectangular faces together, we get the total surface area of the triangular prism:
Total surface area = 141.94 + 438.6 = 580.54 cm^2
Therefore, the total surface area represented by this net of a triangular prism is approximately 580.54 cm^2.
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