Use the image to answer the question. 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 as a triangular prism, how much fabric will be left over? (1 point) Responses 324 cm2 324 cm squared 240 cm2 240 cm squared 184 cm2 184 cm squared 84 cm2
In order to find out how much fabric will be used for the triangular prism tent, we need to calculate the surface area of the prism.
The formula for the surface area of a triangular prism is:
2 * (base area) + (perimeter of base) * (height)
In this case, the base of the prism is a triangle with sides of 18 cm, 18 cm, and 18 cm.
The area of the base triangle can be calculated using Heron's formula:
s = (18 + 18 + 18)/2 = 27
Area = sqrt(27 * 9 * 9 * 9) = 54 * sqrt(27) = 54 * 3sqrt(3) ≈ 93.53 cm²
The perimeter of the base triangle is 18 + 18 + 18 = 54 cm.
The height of the prism is also 18 cm.
Now we can plug these values into the formula for the surface area of the prism:
2 * 93.53 + 54 * 18 ≈ 187.06 + 972 = 1159.06 cm²
Thus, the total fabric used for the tent will be approximately 1159.06 cm².
Since Jordan purchased a piece of fabric that is 18 cm by 18 cm (324 cm²), the leftover fabric will be:
324 cm² - 1159.06 cm² = -835.06 cm²
Since you cannot have negative fabric, there will be no fabric left over.