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
240 centimeters squared
Skip to navigation
It's 84, don't trust penny.
The formula for the surface area of a triangular prism is given by the formula:
Surface Area = 2(base area) + (perimeter of base x height)
The base of the triangular prism is a triangle with sides of 18 cm, 18 cm, and 18 cm. So the base area is calculated as follows:
Base Area = (1/4) x √(sum of sides x difference of sides)²
Base Area = (1/4) x √((18+18+18) x (18+18-18)²
Base Area = (1/4) x √(54 x 18)²
Base Area = (1/4) x √(972)
Base Area = (1/4) x 31.16
Base Area = 77.9 cm²
Now we calculate the perimeter of the base:
Perimeter = 18 + 18 + 18 = 54 cm
Now we calculate the total surface area:
Surface Area = 2(77.9) + (54 x 18)
Surface Area = 155.8 + 972
Surface Area = 1127.8 cm²
Therefore, there will be 1127.8 - 324 = 803.8 cm² of fabric left over.
Thus, the correct answer is: 803.8 centimeters squared.