Perimeter, Area and Volume

In short: Perimeter is the distance around a shape, area is the space inside it, and volume is the space inside a solid. A rectangle's area is length × width, a triangle's area is half of base × height, and a box's volume is length × width × height.

Before you start

• Multiplying decimals, like $6.5\times 4.8$ (see Working with Decimals).
• Metric units of length and capacity (see Metric Units and Conversions).
• Square units: a square 1 cm by 1 cm has an area of 1 cm². Cubic units: a cube 1 cm on each edge has a volume of 1 cm³.

Perimeter

Add up the lengths of all the sides.

A rectangle 7 cm by 4 cm: $7+4+7+4=22$ cm, or $2\times (7+4)=22$ cm.

Area of a rectangle

Area of a triangle

Shaded fractions of a grid

To find what fraction of a grid is shaded, find the shaded area and divide by the total area.

Volume of a box

Quick summary

• Perimeter is the distance around a shape. Add all the sides.
• Area of a rectangle $=l\times w$. Area of a triangle $=\frac{1}{2}\times b\times h$.
• The height of a triangle is at right angles to the base.
• Area is in square units, volume in cubic units.
• Volume of a box $=l\times w\times h$, and 1 cm³ holds 1 mL.

Quiz