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
The total surface area of the triangular prism tent can be calculated as follows:
Total Surface Area = 2(base area) + lateral surface area
The base area of the triangular prism is the area of the triangular face, which is (1/2) * base * height = (1/2) * 4 cm * 6 cm = 12 cm^2.
The lateral surface area of the triangular prism is the area of all three rectangles that make up the sides of the prism. The formula for the lateral surface area of a triangular prism is perimeter of the base * height. The perimeter of the base is 3 * side length = 3 * 7 cm = 21 cm. So, the lateral surface area is 21 cm * 6 cm = 126 cm^2.
Therefore, the total surface area of the triangular prism tent is 2(12 cm^2) + 126 cm^2 = 24 cm^2 + 126 cm^2 = 150 cm^2.
The total area of fabric Jordan has 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 tent from the total fabric area: 324 cm^2 - 150 cm^2 = 174 cm^2.
So, the answer is 174 cm², which is closest to 184 cm².
Therefore, the answer is:
184 cm²