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)
First, calculate the total surface area of the triangular prism. The formula for the surface area of a triangular prism is given by:
Surface Area = 2(Base x Height of Triangle) + (Perimeter of Base x Height of Prism)
Surface Area = 2(4 x 6) + (3 x 7 x 2) = 48 + 42 = 90 cm^2
Now, to find out how much fabric will be used for the tent, we can calculate the surface area of the triangular face and the two rectangular faces:
Surface Area of Triangular Face = 1/2 (Base x Height) = 1/2 (4 x 6) = 12 cm^2
Surface Area of Rectangular Faces = 2 (Base x Height) = 2 (4 x 6) = 48 cm^2
Total Fabric Used = 12 + 48 = 60 cm^2
Therefore, the fabric leftover will be 18 x 18 (total fabric purchased) - 60 (fabric used) = 324 - 60 = 264 cm^2.
So, Jordan will have 264 cm^2 of fabric left over after making the tent for her sister's dolls.