Applications of Surface Area of Prisms Quick Check
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Question
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
184 cm2
184 cm squared
324 cm2
324 cm squared
84 cm2
84 cm squared
240 cm2
To find the surface area of the triangular prism, we need to find the area of the two triangular faces and the three rectangular faces.
The area of each triangular face can be calculated using the formula: (1/2) * base * height
= (1/2) * 4 * 6 = 12 cm^2
There are two triangular faces, so the total area of triangular faces = 2 * 12 = 24 cm^2
The area of each rectangular face can be calculated by finding the area of the rectangle:
1st rectangular face: 4 * 12 = 48 cm^2
2nd rectangular face: 7 * 12 = 84 cm^2
3rd rectangular face: 7 * 4 = 28 cm^2
Total area of rectangular faces = 48 + 84 + 28 = 160 cm^2
Total surface area of the prism = total area of triangular faces + total area of rectangular faces
= 24 + 160 = 184 cm^2
Therefore, Jordan will have 184 cm^2 of fabric left over.
Answer: 184 cm^2