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
84 cm2
84 cm squared
184 cm2
184 cm squared
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The total surface area of the triangular prism can be calculated using the formula:
Surface Area = 2 * base area + lateral area
Base area = 0.5 * base * h = 0.5 * 4 cm * 6 cm = 12 cm^2
Lateral area = perimeter of base * h = 3 * 7 cm * 6 cm = 126 cm^2
Adding these together, we get:
Surface Area = 2 * 12 cm^2 + 126 cm^2 = 150 cm^2
Since Jordan purchased a piece of fabric that is 18 cm by 18 cm (total of 324 cm^2), the amount of fabric leftover will be:
Remaining fabric = Total fabric - Surface Area of the tent
Remaining fabric = 324 cm^2 - 150 cm^2 = 174 cm^2
Therefore, the correct answer is:
184 cm^2