A rectangle has two lengths and two widths. To find the perimeter, add all four sides together.

Formula: $\text{Perimeter of rectangle} = \text{length} + \text{width} + \text{length} + \text{width}$ $\text{Perimeter of rectangle} = 2 \times \text{length} + 2 \times \text{width}$

Worked Example 1

Find the perimeter of a rectangle with length 100 cm and width 40 cm.

Solution

Method 1: Add all sides $100 + 40 + 100 + 40 = 280\text{ cm}$

Method 2: Use the formula $= 2 \times 100 + 2 \times 40$ $= 200 + 80 = 280\text{ cm}$

The perimeter is 280 cm.

Worked Example 2

A football ground is 100 m long and 64 m wide. Find its perimeter.

Solution

$= 2 \times 100\text{ m} + 2 \times 64\text{ m}$ $= 200\text{ m} + 128\text{ m} = 328\text{ m}$

The perimeter is 328 m.

A square has four equal sides. To find the perimeter, multiply the length of one side by 4.

Formula: $\text{Perimeter of square} = 4 \times \text{length}$

Worked Example

A square garden has a side length of 13 m. Find its perimeter.

Solution

$= 4 \times 13\text{ m} = 52\text{ m}$

The perimeter is 52 m.

A triangle has three sides. To find the perimeter, add the lengths of all three sides.

Formula: $\text{Perimeter of triangle} = \text{side}_1 + \text{side}_2 + \text{side}_3$

Worked Example

A triangular field has sides measuring 15 m, 20 m, and 25 m. Find its perimeter.

Solution

$= 15\text{ m} + 20\text{ m} + 25\text{ m} = 60\text{ m}$

The perimeter is 60 m.

Area is the size of the surface inside a flat shape. We measure area in square units like square centimetres (cm²), square metres (m²), or square kilometres (km²).

To find the area of a rectangle, multiply the length by the width.

Formula: $\text{Area of rectangle} = \text{length} \times \text{width}$

Worked Example 1

Find the area of a rectangle with length 9 cm and width 5 cm.

Solution

$= 9\text{ cm} \times 5\text{ cm} = 45\text{ cm}^2$

The area is 45 cm².

Worked Example 2

A classroom floor is 7 m long and 6 m wide. Find the area of the floor.

Solution

$= 7\text{ m} \times 6\text{ m} = 42\text{ m}^2$

The area is 42 m².

All sides of a square are equal. To find the area, multiply the side length by itself.

Formula: $\text{Area of square} = \text{length} \times \text{length}$

Worked Example

A square garden has a side length of 70 m. Find its area.

Solution

$= 70\text{ m} \times 70\text{ m} = 4900\text{ m}^2$

The area is 4900 m².

To find the area of a triangle, multiply the base by the height, then divide by 2 (or multiply by ½).

Formula: $\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}$

Worked Example 1

Find the area of a triangle with base 10 cm and height 7 cm.

Solution

$= \frac{1}{2} \times 10\text{ cm} \times 7\text{ cm}$ $= 5 \times 7 = 35\text{ cm}^2$

The area is 35 cm².

Worked Example 2

A triangular road sign has a base of 40 cm and a height of 55 cm. Find its area.

Solution

$= \frac{1}{2} \times 40\text{ cm} \times 55\text{ cm}$ $= 20 \times 55 = 1100\text{ cm}^2$

The area is 1100 cm².

• Perimeter of rectangle = 2 × length + 2 × width
• Perimeter of square = 4 × length
• Perimeter of triangle = side₁ + side₂ + side₃
• Area of rectangle = length × width
• Area of square = length × length
• Area of triangle = ½ × base × height

In Tanzania, farmers use perimeter and area calculations when fencing their farms or determining how much land they have for planting crops. For example, if a farmer in Morogoro wants to fence a rectangular plot of maize that is 50 metres long and 30 metres wide, they need to calculate the perimeter (2×50 + 2×30 = 160 metres) to know how many metres of fencing wire to buy. Similarly, shop owners at Kariakoo Market calculate the area of their shop floor (in square metres) to know how much tile or cement is needed for renovation.