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 like a triangular prism, how much fabric will be left over?
To calculate the total amount of fabric needed for the triangular prism tent, we first need to find the total surface area of the tent.
The formula for the surface area of a triangular prism is:
SA = 2B + Ph
Where:
SA = Surface area
B = Area of the base (triangle)
P = Perimeter of the base (triangle)
h = Height of the prism
First, let's calculate the area of the base:
Area of a triangle = 1/2 * base * height
Area of the base = 1/2 * 18 cm * 18 cm = 81 cm^2
Now, let's calculate the perimeter of the base:
Perimeter of a triangle = sum of all three sides
Perimeter of the base = 18 cm + 18 cm + 18 cm = 54 cm
Next, let's calculate the total surface area of the tent:
SA = 2(81 cm^2) + 54 cm * h
Since the tent is in the shape of a triangular prism, the height is also 18 cm.
SA = 2(81 cm^2) + 54 cm * 18 cm
SA = 162 cm^2 + 972 cm^2
SA = 1134 cm^2
Therefore, the total amount of fabric needed for the tent is 1134 cm^2. Since Jordan purchased a piece of fabric that is 18 cm by 18 cm, the total area of the fabric is 324 cm^2.
To find out how much fabric will be left over, we subtract the total surface area of the tent from the total area of the fabric:
324 cm^2 - 1134 cm^2 = -810 cm^2
Therefore, there will be -810 cm^2 of fabric left over, which means that Jordan will need additional fabric in order to complete the tent.
Heard it’s 84
I apologize for the mistake in my previous response. Let's recalculate the amount of fabric left over.
The total surface area of the tent is 1134 cm^2, as calculated previously.
The total area of the fabric Jordan purchased is 18 cm * 18 cm = 324 cm^2.
Therefore, to find out how much fabric will be left over, we subtract the total surface area of the tent from the total area of the fabric:
324 cm^2 - 1134 cm^2 = -810 cm^2
It seems like my previous response was correct. There will be -810 cm^2 of fabric left over, indicating that Jordan will need additional fabric in order to complete the tent.
Let me know if there was a misunderstanding or if you would like me to recalculate using different dimensions.