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 324 cm2 324 cm squared 240 cm2 240 cm squared 184 cm2 184 cm squared 84 cm2
To calculate the surface area of the triangular prism tent, we need to find the area of all its faces:
1. The two triangular faces:
- Each face is a right triangle with base = 18 cm and height = 18 cm
- Area of one triangular face = 1/2 * base * height
- Area = 1/2 * 18 cm * 18 cm = 162 cm²
- Total area of both triangular faces = 2 * 162 cm² = 324 cm²
2. The three rectangular faces:
- The top and bottom rectangles have dimensions 18 cm by 18 cm
- Area of each = 18 cm * 18 cm = 324 cm²
- The side rectangle has dimensions 18 cm by 18 cm
- Area = 18 cm * 18 cm = 324 cm²
- Total area of all three rectangles = 2 * 324 cm² + 324 cm² = 648 cm²
Therefore, total fabric needed = 648 cm²
Jordan purchased a 18 cm by 18 cm fabric, so the leftover fabric would be:
Leftover fabric = Total fabric purchased - Fabric needed
Leftover fabric = 18 cm * 18 cm - 648 cm²
Leftover fabric = 324 cm²
Therefore, 324 cm² of fabric will be left over.