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
324 cm2
324 cm squared
240 cm2
240 cm squared
184 cm2
184 cm squared
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page 13 of 13
To find the total surface area of the triangular prism tent, you need to find the area of the two triangular faces and the three rectangular faces.
The area of each triangular face can be calculated by using the formula for the area of a triangle, which is 1/2 * base * height. In this case, the base is 4 cm and the height is 6 cm. So, the area of each triangular face is 1/2 * 4 cm * 6 cm = 12 cm^2. Since there are two triangular faces, the total area is 2 * 12 cm^2 = 24 cm^2.
The three rectangular faces include two that are 12 cm by 6 cm and one that is 4 cm by 6 cm. Thus, the total area of the three rectangular faces is 2 * (12 cm * 6 cm) + 4 cm * 6 cm = 144 cm^2 + 24 cm^2 = 168 cm^2.
Therefore, the total surface area of the triangular prism tent is 24 cm^2 + 168 cm^2 = 192 cm^2.
Since Jordan purchased a piece of fabric that is 18 cm by 18 cm, the total area of the fabric is 18 cm * 18 cm = 324 cm^2.
To find out how much fabric will be left over, subtract the total surface area of the triangular prism tent from the total area of the fabric: 324 cm^2 - 192 cm^2 = 132 cm^2.
Therefore, 132 cm^2 of fabric will be left over.
The closest option is 184 cm^2, but the correct answer based on the calculations is 132 cm^2.