Jordan purchased a piece of fabric that is 18 cm 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 will be left over? The dimensions are 6 cm, 7 cm, 4 cm, and 12 cm
The piece of fabric is 18 cm by 18 cm, so it has an area of 18 cm * 18 cm = 324 cm^2.
To find how much fabric the triangular prism tent will use, we need to find its surface area (not counting the bottom of the tent, since it will not use fabric). It has two triangular faces, each with base 6 cm, height 4 cm. The triangular faces' total area is 2 * (1/2 * 6 cm * 4 cm) = 24 cm^2.
There are 3 rectangular faces on the tent: one with width 6 cm, height 7 cm; one with width 7 cm, height 12 cm; one with width 6 cm, height 12 cm. Their total area is 6 cm * 7 cm + 7 cm * 12 cm + 6 cm * 12 cm = 42 cm^2 + 84 cm^2 + 72 cm^2 = 198 cm^2.
So the tent's total surface area will be 24 cm^2 (for the triangular faces) + 198 cm^2 (for the rectangular faces) = 222 cm^2.
Therefore, after making the tent, Jordan will have 324 cm^2 - 222 cm^2 = 102 cm^2 of fabric left over.