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 like a triangular prism, how much fabric will be left over?

Georgia Milestones Grade 7 Mathematics Formula Sheet

(1 point)
Responses

184 centimeters squared
184 centimeters squared

324 centimeters squared
324 centimeters squared

84 centimeters squared
84 centimeters squared

240 centimeters squared

1 answer

The formula for the surface area of a triangular prism is SA = 2B + Ph, where B is the area of the base, P is the perimeter of the base, and h is the height of the prism.

Since the base of the tent is a triangle with dimensions 18 cm by 18 cm, the area of the base (B) is 0.5(18)(18) = 162 cm^2.

The perimeter of the base (P) is the sum of the three sides of the triangle, which is 18 + 18 + 18 = 54 cm.

The height of the prism is also 18 cm.

Plugging these values into the formula, we get:
SA = 2(162) + (54)(18)
SA = 324 + 972
SA = 1296 cm^2

Therefore, the total amount of fabric needed for the tent is 1296 cm^2. Since Jordan purchased a piece of fabric that is 18 cm by 18 cm, which has an area of 324 cm^2, the amount of fabric left over is:
324 cm^2 - 1296 cm^2 = 84 cm^2

So, the correct answer is 84 centimeters squared.