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
324 cm2
324 cm squared
240 cm2
240 cm squared
84 cm2
84 cm squared
184 cm2
In order to find out the total surface area of the triangular prism, we need to find the lateral area and the area of the two triangular faces.
Lateral area = perimeter of base x height
Lateral area = (4 + 12 + 7 + 7) x 6
Lateral area = 30 x 6
Lateral area = 180 cm2
Area of each triangular face = 0.5 x base x height
Area of each triangular face = 0.5 x 4 x 6
Area of each triangular face = 12 cm2
Total surface area = 2 x (Lateral area) + 2 x (Area of each triangular face)
Total surface area = 2 x 180 + 2 x 12
Total surface area = 360 + 24
Total surface area = 384 cm2
The fabric purchased by Jordan is 18 cm by 18 cm, which has an area of 324 cm2. Therefore, the amount of fabric left over after making the tent shaped as a triangular prism is:
324 cm2 - 384 cm2 = -60 cm2
This calculation means that Jordan does not have enough fabric to make the triangular prism tent according to the provided dimensions.
chose one
324 cm2
324 cm squared
240 cm2
240 cm squared
84 cm2
84 cm squared
184 cm2