Jordan purchase 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 like a triangular prism how much fabric will be left over
In order to calculate the amount of fabric left over, we first need to find the surface area of the triangular prism tent.
The formula for the surface area of a triangular prism is:
Surface Area = 2 * base area + lateral area
The base of the triangular prism is a triangle with base 18 cm and height 18 cm. The formula for the area of a triangle is:
Area = 1/2 * base * height
So, the base area of the triangle is:
1/2 * 18 cm * 18 cm = 162 cm^2
The lateral area of the triangular prism can be calculated by finding the perimeter of the base triangle and multiplying it by the height of the prism. The perimeter of the triangle is:
18 cm + 18 cm + sqrt(18^2 + 9^2) cm = 18 cm + 18 cm + sqrt(585) cm ≈ 60.8 cm
Therefore, the lateral area of the prism is:
60.8 cm * 18 cm = 1094.4 cm^2
Putting it all together:
Surface Area = 2 * 162 cm^2 + 1094.4 cm^2 = 1418.4 cm^2
Now, we can calculate the amount of fabric left over:
Total fabric = 18 cm * 18 cm = 324 cm^2
Leftover fabric = Total fabric - Surface Area = 324 cm^2 - 1418.4 cm^2 = -1094.4 cm^2
Since the leftover fabric is a negative value, it means that Jordan needs additional fabric to cover the surface area of the triangular prism tent.