Question

Use the image to answer the question.
there is a triangular prism there measurements are 4 cm, 12 cm, 7 cm, and 6 cm
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?
A. 324 cm squared
B. 240 cm squared
C. 84 cm squared
D. 184 cm squared

Answer 1

To find the surface area of the triangular prism, we need to find the area of each face and then add them together.

First, find the area of the triangular bases:
Area = (1/2) * base * height
Area = (1/2) * 6 cm * 4 cm = 12 cm squared

Since there are two triangular bases, the total area for the bases is:
2 * 12 cm squared = 24 cm squared

Next, find the area of the three rectangular faces:
Face 1: 12 cm * 7 cm = 84 cm squared
Face 2: 6 cm * 7 cm = 42 cm squared
Face 3: 4 cm * 12 cm = 48 cm squared

Add the areas of the three rectangular faces:
84 cm squared + 42 cm squared + 48 cm squared = 174 cm squared

Now, add the total area for the bases and the total are for the three faces:
24 cm squared (base) + 174 cm squared (faces) = 198 cm squared

Since Jordan purchased fabric that is 18 cm by 18 cm, the total area of the fabric is:
18 cm * 18 cm = 324 cm squared

To find out how much fabric will be left over, subtract the surface area of the triangular prism from the total area of the fabric:
324 cm squared (total fabric) - 198 cm squared (triangular prism) = 126 cm squared

Therefore, the answer is:
C. 126 cm squared