Jordan purchased a piece of fabric that is 18 cm by 18 cm in order to make a tent for her little sisters fools. Using the dimensions for the tent shaped as a triangular prism how much fabric will be left over
To calculate the amount of fabric that will be left over, we first need to calculate the surface area of the triangular prism tent.
The formula to calculate the surface area of a triangular prism is:
Surface Area = 2 * Base Area + lateral area
Given that the base of the prism is a triangle with a base of 18 cm and a height of 18 cm, the formula to calculate the area of the base is
Base Area = 0.5 * base * height
Base Area = 0.5 * 18cm * 18cm
Base Area = 0.5 * 324cm^2
Base Area = 162cm^2
Next, the formula to calculate the lateral area of the triangular prism is:
Lateral Area = perimeter of the base * height of the prism
Lateral Area = base * 3 + 2 * height
Lateral Area = 18cm * 3 + 2 * 18cm
Lateral Area = 54cm + 36cm
Lateral Area = 90cm^2
Now we can calculate the total surface area of the prism:
Surface Area = 2 * 162cm^2 + 90cm^2
Surface Area = 324cm^2 + 90cm^2
Surface Area = 414cm^2
Given that the fabric Jordan purchased is 18 cm by 18 cm, the total fabric area is:
Total Fabric Area = 18cm * 18cm
Total Fabric Area = 324cm^2
To calculate the amount of fabric left over, we subtract the surface area of the prism from the total fabric area:
Fabric Left Over = Total Fabric Area - Surface Area
Fabric Left Over = 324cm^2 - 414cm^2
Fabric Left Over = -90cm^2
Since a negative area doesn't make sense, there will be no fabric left over. The entire piece of fabric will be used to make the tent for her little sister's dolls.