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
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.