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
240 cm squared
184 cm2
184 cm squared
324 cm2
324 cm squared
84 cm2
84 cm squared
To find the total surface area of the triangular prism tent, we need to calculate the area of the two triangular faces and the three rectangular faces.
Area of triangular faces:
2 * (1/2 * base * height) = 2 * (1/2 * 4 * 6) = 2 * 12 = 24 cm squared
Area of rectangular faces:
2 * (base * height) + (base * length) = 2 * (4 * 6) + (4 * 12) = 2 * 24 + 48 = 96 + 48 = 144 cm squared
Total surface area = 24 + 144 = 168 cm squared
Fabric area purchased = 18 * 18 = 324 cm squared
Fabric remaining = Fabric area purchased - Total surface area = 324 - 168 = 156 cm squared