Jordan purchased a pice of fabric that is 18 cm by 18 cm in order to make a tent for her little sisters dolls. Using the dimensions for the tent shaped as a triangular prism, how much fabric will be left over?
324 cm squared
184 cm squared
240 cm squared
84 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 all together.
First, let's find the area of the three rectangular faces:
1. The front and back faces are both rectangles with dimensions 18 cm by 18 cm.
Area of each front/back face = 18 cm * 18 cm = 324 cm^2
Total area of front and back face = 2 * 324 cm^2 = 648 cm^2
2. The bottom face is also a rectangle with dimensions 18 cm by 18 cm.
Area of the bottom face = 18 cm * 18 cm = 324 cm^2
Next, let's find the area of the two triangular faces:
1. The two triangular faces are identical and are right triangles with base and height of 18 cm and 18 cm, respectively.
Area of each triangular face = 0.5 * 18 cm * 18 cm = 162 cm^2
Total area of two triangular faces = 2 * 162 cm^2 = 324 cm^2
Now, we can calculate the total area of the tent:
Total area = Total area of all faces = 648 cm^2 + 324 cm^2 = 972 cm^2
Jordan purchased a fabric with an area of 18 cm by 18 cm, which is 324 cm^2. The total area of the triangular prism tent is 972 cm^2. Therefore, the amount of fabric left over after making the tent would be:
Fabric leftover = Fabric purchased - Total area of tent = 324 cm^2 - 972 cm^2 = -648 cm^2
The negative value for the fabric leftover suggests that there is not enough fabric to make the tent, so in this scenario, Jordan would need additional fabric to complete the tent.