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
324 cm2
324 cm squared
240 cm2
240 cm squared
184 cm2
184 cm squared
84 cm2
84 cm squared
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page 13 of 13
To find the total amount of fabric needed for the triangular prism tent, first find the area of the triangular base:
Area of triangular base = 1/2 * base * height
Area of triangular base = 1/2 * 4 * 6
Area of triangular base = 12 cm²
Then find the area of the three rectangular sides of the prism:
Area of one rectangular side = base * height
Area of one rectangular side = 12 * 6
Area of one rectangular side = 72 cm²
Total area of the three rectangular sides = 72 * 3 = 216 cm²
Adding the area of the triangular base to the area of the three rectangular sides gives the total area of fabric needed:
Total fabric needed = 12 + 216 = 228 cm²
Since Jordan has a piece of fabric that is 18 cm by 18 cm, the total area of fabric is 18 * 18 = 324 cm²
To find the amount of fabric left over, subtract the total fabric needed from the total fabric available:
Fabric left over = Total fabric available - Total fabric needed
Fabric left over = 324 - 228 = 96 cm²
Therefore, the answer is 96 cm² left over.