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
240 cm2
184 cm2
84 cm2
324 cm2
The surface area of a triangular prism is given by the formula: 2(base area) + (perimeter of base * height).
First find the base area:
Base area = 1/2 * base * height = 1/2 * 4 cm * 6 cm = 12 cm2.
Next, find the perimeter of the base:
Perimeter = 3 * side length = 3 * 7 cm = 21 cm.
Now find the surface area of the prism:
Surface Area = 2(12 cm2) + (21 cm * 6 cm) = 24 cm2 + 126 cm2 = 150 cm2.
Since Jordan purchased a fabric piece with an area of 18 cm * 18 cm = 324 cm2, the amount of fabric left over would be: 324 cm2 - 150 cm2 = 174 cm2.
Therefore, Jordan will have 174 cm2 of fabric left over.