The perimeter of the square and rectangle are 44cm each. How much is the area of a rectangle

univerkov | April 11, 2021 | education

The perimeter of the square and rectangle are 44cm each. How much is the area of a rectangle less than the area of a square if one side is 9 cm?

1. Find the side of the square by dividing the perimeter by 4:
44/4 = 11 cm.
2. Find the adjacent side of the rectangle by the formula a = (P – 2b) / 2, where P is the perimeter of the rectangle, and and b are the adjacent sides of the rectangle:
a = (44 – 2 * 9) / 2 = (44 – 18) / 2 = 26/2 = 13 cm.
3. Find the area of the rectangle, which is equal to the product of adjacent sides:
The area of the rectangle = 9 * 13 = 117 cm2.
4. Find the area of a square by squaring its side:
Square area = (11 cm) 2 = 121 cm2.
5. Find how many square centimeters the area of the rectangle is less than the area of the square:
121 – 117 = 4 cm2.
Answer: the area of the rectangle is 4 cm2 less than the area of the square.

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