Geometry Basics — Core Skills

Geometry Basics: Area and Perimeter

Part 1 of 2 — One Skill, One Idea

Two words come up over and over, and they mean different things.

• Perimeter is the distance all the way around the outside. Think of walking around the edge of a yard. It is measured in plain units, like feet.
• Area is how much flat space is inside. Think of the carpet that covers the floor. It is measured in square units, like square feet.

If a question asks how much fence you need, that is perimeter. If it asks how much paint or carpet, that is area.

The formulas you need

• Rectangle area $= \text{length} \times \text{width}$
• Rectangle perimeter $= 2 \times \text{length} + 2 \times \text{width}$
• Square area $= \text{side} \times \text{side}$
• Square perimeter $= 4 \times \text{side}$
• Triangle area $= \frac{1}{2} \times \text{base} \times \text{height}$

A square is a rectangle whose four sides are all the same length, so the rectangle formulas still work on it.

Worked example

A rectangle has length $8$ and width $5$. Find the area and the perimeter.

Area — multiply the two side lengths:

$8 \times 5 = 40$

The area is $40$ square units.

Perimeter — add up all four sides. The rectangle has two sides of length $8$ and two sides of length $5$:

$8 + 8 + 5 + 5 = 26$

The perimeter is $26$ units.

Notice that the two answers are different numbers from the same rectangle. Read the question and decide which one it wants before you start.

Angles and Right Triangles

Part 2 of 2 — Practice

The formulas from Part 1

• Rectangle area $= \text{length} \times \text{width}$
• Square area $= \text{side} \times \text{side}$
• Triangle area $= \frac{1}{2} \times \text{base} \times \text{height}$