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) Responses 184 cm2 184 cm squared 84 cm2 84 cm squared 240 cm2 240 cm squared 324 cm2 324 cm squared
To find the surface area of the triangular prism tent, we need to calculate the area of each face and then add them together.
The tent has 5 faces - 2 triangular faces and 3 rectangular faces.
The triangular faces have the same base and height, which can be calculated as:
Base = 18 cm
Height = (1/2)*18 = 9 cm
Area of one triangular face = (1/2)*base*height = (1/2)*18*9 = 81 cm^2
Since there are 2 triangular faces, the total area for both is 2*81 = 162 cm^2
The rectangular faces have dimensions 18 cm by 9 cm and their total area is:
2 * (18 * 9) = 2 * 162 = 324 cm^2
Adding the areas of all the faces: 162 (triangular faces) + 324 (rectangular faces) = 486 cm^2
Since Jordan purchased a piece of fabric that is 18 cm by 18 cm, the total area of the fabric is 18*18 = 324 cm^2
Therefore, the amount of fabric left over will be 324 (total fabric) - 486 (tent surface area) = -162 cm^2
So, the correct answer is: 184 cm squared.