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?
h: 6cm , 7cm
b: 4cm
w: 12cm
To find the amount of fabric left over, we first need to calculate the total surface area of the triangular prism tent.
The formula for the surface area of a triangular prism is:
Surface Area = 2(base x height) + (width x height) + (perimeter of base x height)
Given:
- b: 4cm
- h: 6cm
- w: 12cm
Calculating the total surface area:
Base area = 1/2 * base * height
Base area = 1/2 * 4 * 6
Base area = 12 cm²
Width area = base * width
Width area = 4 * 12
Width area = 48 cm²
Height area = height * width
Height area = 6 * 12
Height area = 72 cm²
Perimeter of base = sum of the lengths of its sides
Perimeter of base = 4 + 4 + 6 + 6
Perimeter of base = 20 cm
Surface Area = 2(12) + 48 + 20 * 6
Surface Area = 24 + 48 + 120
Surface Area = 192 cm²
The total surface area of the tent is 192 cm². Since the piece of fabric Jordan purchased is 18 cm by 18 cm (324 cm²), the amount of fabric left over is:
324 cm² - 192 cm² = 132 cm²
Jordan will have 132 cm² of fabric left over after making the tent.