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
provided details: (6cm, 7cm, 4cm, 12cm.)
To find the surface area of the tent shaped like a triangular prism, we need to find the area of all the faces and then subtract the area of the base (since it is already used).
The surface area of a triangular prism can be found using the formula:
Surface area = 2(base area) + (perimeter of base x height)
First, we need to find the area of the triangular base. The base has dimensions of 6 cm, 7 cm, and 4 cm. Using Heron's formula to find the area of the base:
s = (6+7+4)/2 = 8.5
Area = sqrt(8.5(8.5-6)(8.5-7)(8.5-4)) = sqrt(8.5*2.5*1.5*4.5) = sqrt(114.84375) ≈ 10.716 cm²
Now, find the perimeter of the base:
Perimeter = 6 + 7 + 4 = 17 cm
Now, we can find the surface area of the tent shaped like a triangular prism:
Surface area = 2(10.716) + (17 x 12) = 21.432 + 204 = 225.432 cm²
Since Jordan purchased a piece of fabric that is 18 cm by 18 cm (324 cm²) and the surface area of the tent is 225.432 cm², the amount of fabric left over will be:
324 cm² - 225.432 cm² = 98.568 cm²
Therefore, the correct answer is 100 centimeters squared, or "100 centimeters squared".