Justin purchases fabric that is 18 cm by 18 cm to make a tent for dolls. The tent is shaped like a prism that is 7 by 4 by 12 by 6 cm tall. how much fabric is left over
To calculate the amount of fabric left over, we first find the surface area of the prism-shaped tent.
The surface area of a prism can be found by calculating the area of each face and adding them together.
The prism has 2 rectangular faces that are 7 cm by 4 cm each:
2(7 cm x 4 cm) = 2(28 cm) = 56 cm
The prism has 2 rectangular faces that are 7 cm by 12 cm each:
2(7 cm x 12 cm) = 2(84 cm) = 168 cm
The prism has 2 rectangular faces that are 4 cm by 12 cm each:
2(4 cm x 12 cm) = 2(48 cm) = 96 cm
Adding these areas together, we get:
56 cm + 168 cm + 96 cm = 320 cm
Therefore, the total surface area of the prism-shaped tent is 320 square cm.
The fabric Justin purchased is 18 cm by 18 cm, so the area of fabric he has to work with is:
18 cm x 18 cm = 324 cm
To find out how much fabric is left over after making the tent, we subtract the total surface area of the prism from the area of the fabric:
324 cm - 320 cm = 4 cm
Justin will have 4 square cm of fabric left over after making the tent for the dolls.