Question
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An illustration shows a 3 D triangular prism. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 4 centimeters. The perpendicular height h measures 6 centimeters, and the sides of the triangular face measures 7 centimeters.
Jordan purchased a piece of fabric that is 18 cm by 18 cm in order to make a tent for her little sister’s dolls. Using the dimensions for the tent shaped as a triangular prism, how much fabric will be left over?
An illustration shows a 3 D triangular prism. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 4 centimeters. The perpendicular height h measures 6 centimeters, and the sides of the triangular face measures 7 centimeters.
Jordan purchased a piece of fabric that is 18 cm by 18 cm in order to make a tent for her little sister’s dolls. Using the dimensions for the tent shaped as a triangular prism, how much fabric will be left over?
Answers
Answer
A. 184
B. 240
C. 84
D. 324
B. 240
C. 84
D. 324
Answered by
GPT 3.5
To find the surface area of the triangular prism, we first need to find the area of the triangular base.
The area of a triangle is calculated as 1/2 * base * height. In this case, the base is 4 cm and the height is 6 cm, so the area of the triangular base is 1/2 * 4 * 6 = 12 cm².
Since the triangular prism has 2 identical triangular bases, the total area of both bases is 2 * 12 = 24 cm².
Next, we calculate the lateral surface area of the prism. The lateral surface area of a triangular prism is given by the formula: perimeter of the base * height of the prism.
The perimeter of the triangular face is 3 * 7 = 21 cm. Therefore, the lateral surface area is 21 cm * 6 cm = 126 cm².
The total surface area of the prism is the sum of the area of both bases and the lateral surface area: 24 cm² + 126 cm² = 150 cm².
Since Jordan's piece of fabric is 18 cm by 18 cm, the total area is 18 * 18 = 324 cm².
Therefore, after making the tent for her sister's dolls, Jordan will have 324 cm² - 150 cm² = 174 cm² of fabric left over.
The area of a triangle is calculated as 1/2 * base * height. In this case, the base is 4 cm and the height is 6 cm, so the area of the triangular base is 1/2 * 4 * 6 = 12 cm².
Since the triangular prism has 2 identical triangular bases, the total area of both bases is 2 * 12 = 24 cm².
Next, we calculate the lateral surface area of the prism. The lateral surface area of a triangular prism is given by the formula: perimeter of the base * height of the prism.
The perimeter of the triangular face is 3 * 7 = 21 cm. Therefore, the lateral surface area is 21 cm * 6 cm = 126 cm².
The total surface area of the prism is the sum of the area of both bases and the lateral surface area: 24 cm² + 126 cm² = 150 cm².
Since Jordan's piece of fabric is 18 cm by 18 cm, the total area is 18 * 18 = 324 cm².
Therefore, after making the tent for her sister's dolls, Jordan will have 324 cm² - 150 cm² = 174 cm² of fabric left over.
Answered by
GPT 3.5
C. 84
After making the tent for her little sister's dolls in the shape of a triangular prism, Jordan will have 84 cm² of fabric left over.
After making the tent for her little sister's dolls in the shape of a triangular prism, Jordan will have 84 cm² of fabric left over.
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