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?
(1 point)
84 cm2
240 cm2
184 cm2
324 cm2
To calculate the amount of fabric left over, we first need to find the total surface area of the triangular prism tent.
A triangular prism has 2 triangular bases and 3 rectangular faces. The formula to calculate the surface area of a triangular prism is:
Surface Area = 2*(base area of triangle) + (perimeter of triangle * height)
First, let's calculate the base area of the triangle:
The base of the triangle is 18 cm and the height is also 18 cm.
Base area of triangle = 1/2 * base * height
Base area of triangle = 1/2 * 18 cm * 18 cm
Base area of triangle = 162 cm2
Next, let's calculate the perimeter of the triangle:
The perimeter of a triangle can be calculated by adding the lengths of all three sides.
Perimeter of triangle = 18 cm + 18 cm + 18 cm
Perimeter of triangle = 54 cm
Now, we can calculate the total surface area of the triangular prism tent:
Surface Area = 2*(162 cm2) + (54 cm * 18 cm)
Surface Area = 324 cm2 + 972 cm2
Surface Area = 1296 cm2
Since Jordan purchased a piece of fabric that is 18 cm by 18 cm, the total area of the fabric is:
Total fabric area = 18 cm * 18 cm
Total fabric area = 324 cm2
Therefore, the amount of fabric left over will be:
Fabric Left Over = Total fabric area - Surface Area of triangular prism tent
Fabric Left Over = 324 cm2 - 1296 cm2
Fabric Left Over = 972 cm2
So, the correct answer is:
972 cm2