Jordan purchased a piece of fabric that is 18 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 me left over?
To find out how much fabric will be left over, we first need to calculate the total amount of fabric Jordan will use to make the tent.
The formula for the surface area of a triangular prism is:
2 x base area + lateral area
Given that the base of the tent is a triangle with a base of 18 cm and a height of 18 cm, the base area can be calculated as:
base area = 1/2 x base x height = 1/2 x 18 cm x 18 cm = 162 sq cm
The lateral area of the tent can be calculated as:
lateral area = base perimeter x height = (18 cm + 18 cm + 18 cm) x 18 cm = 54 cm x 18 cm = 972 sq cm
Therefore, the total amount of fabric Jordan will use to make the tent is:
2 x base area + lateral area = 2 x 162 sq cm + 972 sq cm = 1296 sq cm
Since Jordan purchased a piece of fabric that is 18 by 18 cm, the total amount of fabric she has is:
18 cm x 18 cm = 324 sq cm
To find out how much fabric will be left over, we subtract the total amount of fabric she will use from the total amount of fabric she has:
324 sq cm - 1296 sq cm = -972 sq cm
Since the result is negative, it means that Jordan will need more fabric in order to make the tent and no fabric will be left over.