Rectangles and Squares

Rectangles and squares are described together because the formulas for finding their area and perimeter are the same, despite them having a few differences.

Rectangle: a quadrilateral with opposite sides equal and four right angles

Square: a quadrilateral with four equal sides and four right angles

A square is a special type of rectangle, but a rectangle is not a square (because rectangles do not have four equal sides).

Area of a rectangle or a square: length x width (L x W)

Perimeter of a rectangle or square: add all the sides

For a rectangle, perimeter could also be written 2L + 2W.

For a square, perimeter could be written as 4 x s (side length).

Example math problems related to squares and rectangles:

  1. If a rectangle has length 19 cm, and width 23 cm, what is its area and perimeter?
    • To find area, all we have to do is multiply 19 x 23 to get 437 sq. cm.
    • For perimeter, we know that a rectangle has opposite sides equal. Therefore, two of those sides are 19 cm and two are 23 cm. Just add the sides together: 19 + 19 + 23 + 23 = 84 cm.
    • A = 437 sq. cm, P = 84 cm
  2. If a square sheet of paper has a side of 24 cm, what is its area and perimeter?
    • To find area, we multiply length x width. We know that a square has all sides equal, so we multiply 24 x 24 to get 576 sq. cm.
    • For perimeter, we know that all four sides of the square are equal. Therefore we can either add 24 four times, or multiply 4 x 24 to get 96 cm.
    • A = 576 sq. cm, P = 96 cm