Area and Perimeter of Rectangles

Understanding how to calculate the area and perimeter of rectangles and squares is an essential geometry skill. Once you know the basic formulas, you can work backward to find missing dimensions or even find the measurements of complex shapes made from multiple rectangles.

The Basic Formulas

Perimeter is the total distance around the outside of a shape.

• Rectangle: Add all four sides, or use the formula $P = (2 \times l) + (2 \times w)$ (where $l$ is length and $w$ is width).
• Square: Since all four sides are equal, $P = 4 \times s$ (where $s$ is the side length).

Area is the total space inside a shape, measured in square units.

• Rectangle: Multiply the length by the width: $A = l \times w$
• Square: Multiply the side length by itself: $A = s \times s$

Finding Missing Dimensions

Sometimes, you are given the area or perimeter and only one side length. You can use algebraic reasoning to work backward and find the missing measurement.

Example 1: Missing Width A rectangle has an area of $48$ sq cm and a length of $8$ cm. What is the width? We know $A = l \times w$. Plug in the numbers you know: $48 = 8 \times w$ To find $w$, divide the area by the length: $w = 48 \div 8 = 6$ The width is $6$ cm.

Example 2: Missing Side of a Square A square has a perimeter of $52$ cm. What is the side length? We know $P = 4 \times s$. Plug in the perimeter: $52 = 4 \times s$ Divide by $4$ to find one side: $s = 52 \div 4 = 13$ The side length is $13$ cm.

Composite Figures

Composite figures are complex shapes made up of two or more simple shapes, like an L-shaped polygon.

Finding Perimeter of a Composite Figure: To find the perimeter, simply add up all the outside edges of the shape. If a side length is missing, look at the parallel sides opposite to it. The total length of the smaller parallel segments on one side will equal the total length of the single long segment on the opposite side.

Finding Area of a Composite Figure: To find the area, break the figure apart!

1. Draw a line to split the composite figure into two separate, simple rectangles.
2. Find the area of the first rectangle ($l \times w$).
3. Find the area of the second rectangle ($l \times w$).
4. Add the two areas together to get the total area of the composite figure.