Use the image to answer the question.
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)
184 cm2
240 cm2
84 cm2
324 cm2
To find the amount of fabric used for the triangular prism tent, we need to find the total surface area of the prism.
The formula for the surface area of a triangular prism is:
Surface Area = 2*(base area of triangle) + (perimeter of triangle)*(height)
First, let's find the base area of the triangle:
Base area = (1/2)*(18)*(18) = 162 cm^2
Next, let's find the perimeter of the triangle:
Perimeter = 18 + 18 + 18 = 54 cm
Now, we need to find the height of the prism. Since the fabric is 18 cm long, the height of the prism will also be 18 cm.
Now we can plug these values into the formula for surface area of the prism:
Surface Area = 2*(162) + (54)*(18) = 324 + 972 = 1296 cm^2
Since Jordan purchased fabric that is 18 cm by 18 cm, the total fabric area she purchased is 18*18 = 324 cm^2.
To find out how much fabric will be left over, we subtract the surface area of the prism from the total fabric area:
Leftover fabric = Total fabric area - Surface area of prism
Leftover fabric = 324 - 1296 = -972 cm^2
Therefore, there will be 972 cm^2 of fabric leftover after making the triangular prism tent, which corresponds to 972 cm^2 option.