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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?

Answer 1

To find the surface area of the triangular prism, we first need to find the area of the triangular base.

The area of a triangle is calculated as 1/2 * base * height. In this case, the base is 4 cm and the height is 6 cm, so the area of the triangular base is 1/2 * 4 * 6 = 12 cm².

Since the triangular prism has 2 identical triangular bases, the total area of both bases is 2 * 12 = 24 cm².

Next, we calculate the lateral surface area of the prism. The lateral surface area of a triangular prism is given by the formula: perimeter of the base * height of the prism.

The perimeter of the triangular face is 3 * 7 = 21 cm. Therefore, the lateral surface area is 21 cm * 6 cm = 126 cm².

The total surface area of the prism is the sum of the area of both bases and the lateral surface area: 24 cm² + 126 cm² = 150 cm².

Since Jordan's piece of fabric is 18 cm by 18 cm, the total area is 18 * 18 = 324 cm².

Therefore, after making the tent for her sister's dolls, Jordan will have 324 cm² - 150 cm² = 174 cm² of fabric left over.

Answer 2

A. 184
B. 240
C. 84
D. 324

Answer 3

C. 84

After making the tent for her little sister's dolls in the shape of a triangular prism, Jordan will have 84 cm² of fabric left over.