Jordan purchased a piece of fabric that is 18 by 18 cm in order to make a tent for her little sisters dolls. Using the dimensions for the tent shaped as a triangular prism, how much fabric will me left over?
A. 184 cm²
B. 324 cm²
C. 240 cm²
D.84 cm²
To find the amount of fabric used for the triangular prism tent, we first need to calculate the surface area of the prism.
The formula for the surface area of a triangular prism is:
Surface Area = 2*(base area of triangle) + (perimeter of triangle * height of prism)
Given that the dimensions of the fabric are 18cm by 18cm, we can assume that the base of the triangular prism is a right-angled triangle with legs of 18cm.
First, calculate the base area of the triangle:
Base area = (1/2) * base * height
Base area = (1/2) * 18 * 18
Base area = 81 cm²
Next, calculate the perimeter of the triangle:
Perimeter = base1 + base2 + hypotenuse
Perimeter = 18 + 18 + 18√2 (using Pythagoras theorem)
Perimeter = 36 + 18√2
Now, we can calculate the surface area of the triangular prism:
Surface Area = 2*(81) + (36 + 18√2) * 18
Surface Area = 162 + (36 + 18√2) * 18
Surface Area ≈ 240 cm²
Therefore, the amount of fabric used for the triangular prism tent is approximately 240 cm². Since Jordan purchased fabric that is 18 by 18 cm, the fabric used matches the dimensions of the tent. Therefore, no fabric will be left over. The correct answer is C. 240 cm².