Jordan purchased a piece of fabric that is 18 cm x 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?

Answer 1

To calculate how much fabric will be used for the triangular prism tent, we first need to find the surface area of the prism which will be covered by the fabric.

The formula for the surface area of a triangular prism is:

Surface Area = 2 * base area of the triangle + perimeter of the base * height of the prism

The base of the triangle will be half of the fabric piece, as it is a right-angled triangle.

Base Area of the Triangle = (1/2) * 18 cm * 18 cm = 162 cm^2

Now, we need to calculate the perimeter of the base which is the sum of all three sides of the triangle.

Perimeter of the base = 18 cm + 18 cm + hypotenuse

The hypotenuse can be calculated using the Pythagorean theorem:

hypotenuse = sqrt(18^2 + 18^2) = sqrt(648) = 18√2 cm

Perimeter of the base = 18 cm + 18 cm + 18√2 cm = 36 + 18√2 cm

Now, the height of the prism is also 18 cm.

Surface Area = 2 * 162 cm^2 + (36 + 18√2) cm * 18 cm
Surface Area = 324 cm^2 + (36 + 18√2) * 18 cm
Surface Area = 324 cm^2 + 648 + 324√2 cm
Surface Area = 972 + 324√2 cm^2

So, the total fabric used will be 24 + 18√2 square cm.

Since the total area of fabric Jordan purchased was 18 cm * 18 cm = 324 cm^2, we can now calculate the remaining fabric:

Remaining Fabric = Total Fabric - Fabric Used
Remaining Fabric = 324 cm^2 - 972 + 324√2 cm^2
Remaining Fabric = 324 cm^2 - 972 cm^2 - 324√2 cm^2
Remaining Fabric = -648 + 324√2 cm^2

Therefore, Jordan will require more fabric to make the triangular prism tent for her sister’s dolls.