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 to make a tent for her little sister’s dolls. Using the dimensions for the tent-shaped triangular prism, how much fabric will be left over?
To find out how much fabric will be used for the tent-shaped triangular prism, we need to calculate the surface area of each face of the prism and add them together.
The formula for the surface area of a triangular prism is:
2 * base area + base perimeter * height
First, we calculate the base area of the triangular prism:
Base area = (1/2) * base * height
Base area = (1/2) * 4 * 6
Base area = 12 cm^2
Next, we calculate the base perimeter of the triangular prism:
Base perimeter = 3 * side
Base perimeter = 3 * 7
Base perimeter = 21 cm
Now, we calculate the total surface area of the triangular prism:
2 * 12 + 21 * 12
= 24 + 252
= 276 cm^2
Jordan's fabric is 18 cm by 18 cm, so the total fabric area is:
18 * 18 = 324 cm^2
Therefore, the amount of fabric leftover after making the tent-shaped triangular prism would be:
324 - 276 = 48 cm^2
Jordan will have 48 cm^2 of fabric leftover.