Chapter 6: Perimeter and Area

When you walk around a park you measure its perimeter , the length of its boundary. When you lay grass inside the park you measure its area , the size of the surface enclosed. Perimeter and area are two different ways of measuring the same shape, and confusing them is one of the most common slips in geometry.

Both ideas turn up everywhere. A tailor needs the perimeter of a piece of cloth to know how much border tape to buy. A farmer needs the area of a field to know how much seed to scatter. A painter needs both: perimeter for the cost of edging, area for the cost of paint.

In this chapter we work with the most familiar shapes , squares, rectangles, and triangles , and develop simple formulas. Then we tackle irregular shapes, by splitting them into pieces or by counting unit squares on a grid. By the end you will be able to estimate the area of any reasonable region you come across.

What's inside

Perimeter , what it means and how to measure it.
Area , the count of unit squares.
Perimeter and area of rectangles and squares.
Area of triangles.
Areas of irregular shapes , by splitting and by counting.

Key results / Formula card

Shape	Perimeter	Area
Square (side $s$ )	$4s$	$s^2$
Rectangle (length $l$ , breadth $b$ )	$2(l + b)$	$l \times b$
Triangle (base $b$ , height $h$ )	sum of $3$ sides	$\frac{1}{2} \times b \times h$
Right triangle (legs $a$ and $b$ )	$a + b + c$ (with $c$ the hypotenuse)	$\frac{1}{2} a b$

Units:

Perimeter is in length units: cm, m, km.
Area is in square units: cm², m², km².

Conversions: $1 \text{ m}^2 = 100 \times 100 = 10{,}000 \text{ cm}^2$ . $1 \text{ km}^2 = 1{,}000{,}000 \text{ m}^2$ .

How to read this chapter

Use graph paper for every example you can. Counting unit squares is the most reliable way to build intuition. When you trust a formula, that is the day you have understood it.

Chapter 6: Perimeter and Area

What's inside

Key results / Formula card

How to read this chapter

Sub-topics

Practice quiz