GoalFind the area and the perimeter of rectangles and squares, and a missing side.
New words
area · the amount of flat space inside a shape, in square unitsperimeter · the distance around a shapesquare centimetre · the area of a square with sides 1 cm long
Explanation
Area and perimeter measure different things. Area is the space inside a shape. For a rectangle, multiply the length by the width. A rectangle 7 cm long and 4 cm wide has area 7 × 4 = 28 square cm. Perimeter is the distance around the shape. Add all four sides: 7 + 4 + 7 + 4 = 22 cm. We write the area in square units and the perimeter in plain units, such as cm. A square has four equal sides, so a square with side 6 m has area 6 × 6 = 36 square metres and perimeter 6 + 6 + 6 + 6 = 24 m. If we know the area and one side, we can find the other side by dividing: if the area is 36 square cm and the length is 9 cm, the width is 36 ÷ 9 = 4 cm.
Worked examples
Work
Answer
Area
7 × 4
28 square cm
Perimeter
7 + 4 + 7 + 4
22 cm
Find the area and perimeter of this rectangle. Area: 7 × 4 = 28 square cm. Perimeter: 7 + 4 + 7 + 4 = 22 cm.
A garden is 9 m long and 6 m wide. Its area is 9 × 6 = 54 square metres. A fence around it needs the perimeter: 9 + 6 + 9 + 6 = 30 m.
A rectangle has area 36 square cm and length 9 cm. Divide to find the width: 36 ÷ 9 = 4 cm. Check: 9 × 4 = 36.
Class activity
Garden plans. Use squared paper. Draw three different rectangles on it, one square unit being one square. For each, count the squares to find the area and add the sides to find the perimeter. Can you draw two rectangles with the same area but different perimeters?
Practice
1
A rectangle is 8 cm long and 3 cm wide. Find its area and perimeter.
Area: 8 × 3 = 24 square cm. Perimeter: 8 + 3 + 8 + 3 = 22 cm.
2
A square has sides of 6 m. Find its area and its perimeter.
