12 cm
7 cm
6 cm
4 cm
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?
a. 84 cm^2
b. 184 cm^2
c. 249 cm^2
d. 324 cm^2
To find how much fabric will be used for the triangular prism tent, we need to calculate the surface area of all the sides.
The triangular prism has 3 rectangular sides and 2 triangular sides.
The rectangular sides:
- Length = 18 cm, Width = 7 cm
Each rectangular side would have an area of 18 cm * 7 cm = 126 cm^2
Since there are 2 rectangular sides, the total area for both would be 2 * 126 cm^2 = 252 cm^2
The triangular sides:
- Base = 18 cm, Height = 12 cm
Each triangular side would have an area of 0.5 * base * height = 0.5 * 18 cm * 12 cm = 108 cm^2
Since there are 2 triangular sides, the total area for both would be 2 * 108 cm^2 = 216 cm^2
Now, add the areas of all the sides together:
252 cm^2 (rectangular sides) + 216 cm^2 (triangular sides) = 468 cm^2
Since the total fabric purchased by Jordan was 18 cm * 18 cm = 324 cm^2
To find how much fabric will be left over, we subtract the total fabric used for the tent from the total fabric purchased:
324 cm^2 (total fabric purchased) - 468 cm^2 (total fabric used for the tent) = -144 cm^2
The negative value indicates that there would be 144 cm^2 less fabric than needed to make the tent. However, fabric cannot be negative, so this likely means that the tent cannot be made with the fabric purchased and there would be no fabric left over.
Therefore, the correct answer is not listed in the options given as there would be no fabric left over for making the tent with the dimensions provided.