Use the image to answer the question.
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?
(1 point)
Responses
240 cm2
240 cm squared
84 cm2
84 cm squared
184 cm2
184 cm squared
324 cm2
324 cm squared
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To find the amount of fabric needed for the tent shaped as a triangular prism, we need to calculate the total surface area of the prism.
The formula for the total surface area of a triangular prism is:
Total Surface Area = 2 * (base area of the triangle) + (perimeter of the triangle) * (height of the prism)
First, calculate the base area of the triangle:
Base area = (1/2) * base * height
Base area = (1/2) * 4 cm * 6 cm
Base area = 12 cm2
Next, calculate the perimeter of the triangular face:
Perimeter = 3 * side
Perimeter = 3 * 7 cm
Perimeter = 21 cm
Now, calculate the total surface area of the prism:
Total Surface Area = 2 * 12 cm2 + 21 cm * 6 cm
Total Surface Area = 24 cm2 + 126 cm2
Total Surface Area = 150 cm2
The amount of fabric needed for the tent is 150 cm2. Since Jordan purchased a piece of fabric that is 18 cm by 18 cm (324 cm2), the amount of fabric left over will be:
324 cm2 - 150 cm2 = 174 cm2
Therefore, the correct answer is:
184 cm2