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?
To calculate how much fabric will be left over, we need to find the surface area of the triangular prism that will be made by Jordan.
A triangular prism has two triangular faces and three rectangular faces. The formula for the surface area of a triangular prism is given by:
Surface Area = 2 * base area of the triangle + perimeter of the triangle * height of the prism + base area of the rectangle * 2
Given that the dimensions of the fabric are 18 cm by 18 cm, the base area of the triangle will be:
Base area of triangle = 1/2 * base * height = 1/2 * 18 * 18 = 162 cm^2
The perimeter of the triangle will be the sum of all three sides, which are all 18 cm:
Perimeter of triangle = 18 + 18 + 18 = 54 cm
The height of the prism is also 18 cm.
The base area of the rectangle will be the length multiplied by the width:
Base area of rectangle = 18 * 18 = 324 cm^2
Therefore, the surface area of the triangular prism is:
Surface Area = 2 * 162 + 54 * 18 + (2 * 324) = 324 + 972 + 648 = 1944 cm^2
The total area of the fabric is 18 cm by 18 cm, which is equal to 324 cm^2. Therefore, the amount of fabric left over will be:
324 - 1944 = -1620 cm^2
Since fabric cannot have a negative area, this means that Jordan will need more fabric in order to make the tent as specified.