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
84 cm2
84 cm squared
184 cm2
184 cm squared
324 cm2
324 cm squared
240 cm2
240 cm squared
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To find the surface area of the triangular prism, we need to calculate the area of the two triangular faces and the three rectangular faces.
Area of triangular faces:
1/2 * base * height
1/2 * 4 * 6 = 12 cm²
Area of rectangular faces:
length * width
4 * 12 = 48 cm² (two of these)
Total surface area = 2(12) + 3(48) = 120 cm²
Area of fabric left over = Total fabric area - Surface area of the triangular prism
Area of fabric left over = 324 cm² - 120 cm²
Area of fabric left over = 204 cm²
Therefore, Jordan will have 204 cm² of fabric left over.