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
240 cm2
240 cm squared
324 cm2
324 cm squared
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page 13 of 13
To find the total surface area of the triangular prism tent, we need to calculate the area of each face and then add them together.
First, let's calculate the area of the triangular face:
Area = (1/2) * base * height
Area = (1/2) * 4 * 6
Area = 12 cm squared
Since there are two identical triangular faces, the total area for the triangular faces is:
12 cm squared + 12 cm squared = 24 cm squared
Now, let's calculate the area of the rectangular faces:
Area = length * height
Area = 12 * 6
Area = 72 cm squared
Since there are three rectangular faces, the total area for the rectangular faces is:
3 * 72 cm squared = 216 cm squared
Now, add the total area of the triangular faces and the total area of the rectangular faces:
24 cm squared + 216 cm squared = 240 cm squared
Therefore, the total fabric needed for the tent is 240 cm squared. Since Jordan purchased a fabric that is 18 cm by 18 cm, the total fabric available is 18 cm * 18 cm = 324 cm squared.
Subtracting the total fabric needed for the tent from the total fabric available:
324 cm squared - 240 cm squared = 84 cm squared
Therefore, Jordan will have 84 cm squared of fabric left over.