Jordan purchased a piece 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 will be left over?
84cm2
Assuming that the tent has a triangular base and sloping sides, we need to first calculate the area of the base triangle. Since the base is an equilateral triangle (since it has equal sides), we can use the formula for the area of an equilateral triangle:
Area of equilateral triangle = (√3 / 4) x side^2
where side is the length of one side of the triangle.
We know that the side of the base is 18 cm, so:
Area of base triangle = (√3 / 4) x 18^2
= (√3 / 4) x 324
= 81√3 cm2
Next, we need to calculate the area of each sloping side of the tent. We can use the formula for the area of a triangle:
Area of triangle = (1/2) x base x height
Since we know the height of each sloping side is also 18 cm, we only need to find the length of the base of each side. This length will be the same as the length of one side of the base triangle (18 cm). So:
Area of each sloping side = (1/2) x 18 x 18
= 162 cm2 (for each side)
Finally, we need to add up the areas of the base triangle and both sloping sides, and subtract this total from the total area of the fabric:
Total area of tent = Area of base triangle + 2 x Area of sloping side
= 81√3 + 2 x 162
= 81√3 + 324
= 405.02 cm2 (rounded to two decimal places)
Area left over = Area of fabric - Total area of tent
= 324 - 405.02
= -81.02 cm2
Since we got a negative answer, this means that the fabric is not enough to make the tent. Therefore, Jordan will need to purchase more fabric.