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?
324 cm2
184 cm2
84 cm2
240 cm2
The total surface area of the triangular prism is calculated by adding the areas of the three rectangular faces and the two triangular faces.
The area of the rectangular faces can be calculated as 12 cm (length) x 6 cm (height) = 72 cm^2 for each of the two rectangular faces, totaling 144 cm^2.
The area of the two triangular faces can be calculated as 0.5 x 4 cm (base) x 6 cm (height) = 12 cm^2 for each of the two triangular faces, totaling 24 cm^2.
Therefore, the total surface area of the triangular prism is 144 cm^2 + 24 cm^2 = 168 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 x 18 cm = 324 cm^2.
Therefore, the amount of fabric left over after making the tent will be 324 cm^2 (fabric purchased) - 168 cm^2 (total surface area of the tent) = 156 cm^2.
Therefore, there will be 156 cm^2 of fabric left over.