Discover Mathematics P4: Term 1, Unit 4, Lessons 1–5
GoalFind a missing side from the area or the perimeter, split odd shapes into rectangles, and see what doubling the sides does.
New words
missing side · a side whose length we do not know and want to findcomposite shape · a shape made of two or more simpler shapes, such as an L shapedouble · to make twice as big: multiply by 2
Explanation
If we know the area and one side of a rectangle, we divide to find the other side: w = A ÷ l. A rectangle has an area of 48 m² and a length of 8 m, so w = 48 ÷ 8 = 6 m. If we know the perimeter and one side, first find half the perimeter, which is l + w. A rectangle has a perimeter of 30 cm and a length of 9 cm: l + w = 30 ÷ 2 = 15 cm, so w = 15 − 9 = 6 cm. For an odd shape such as an L, draw a dashed line to split it into rectangles, find each area and add. Its perimeter is the sum of all its outside sides. When both sides of a rectangle are doubled, the perimeter doubles but the area becomes 4 times as big.
Worked examples
A rectangle has an area of 48 m² and a length of 8 m. The width is 48 ÷ 8 = 6 m. Check: 8 × 6 = 48.
The L-shaped garden has been split by the dashed line into a 10 m by 4 m rectangle and a 4 m by 3 m rectangle. The areas are 10 × 4 = 40 m² and 4 × 3 = 12 m². The whole area is 40 + 12 = 52 m². The perimeter is 10 + 4 + 6 + 3 + 4 + 7 = 34 m.
Rectangle
Perimeter
Area
3 by 2
10
6
6 by 4
20
24
Double the sides of a 3 cm by 2 cm rectangle to 6 cm by 4 cm. The perimeter goes from 10 cm to 20 cm, which is twice as much. The area goes from 6 cm² to 24 cm², which is 4 times as much.
Class activity
Design a plan. Draw an L-shaped room on squared paper, with measurements in metres. Split it into two rectangles, find the area of the floor and the perimeter for the skirting board. Then double all sides and see what happens to the area.
Practice
1
A rectangle has an area of 72 cm² and a width of 8 cm. Find its length.
72 ÷ 8 = 9 cm.
2
A rectangle has a perimeter of 26 m and a length of 8 m. Find its width.
l + w = 13, so w = 13 − 8 = 5 m.
3
A square has a perimeter of 36 cm. What is its side and its area?
Side 36 ÷ 4 = 9 cm. Area 9 × 9 = 81 cm².
4
Split this shape into rectangles to find its area: an L made of a 6 m by 2 m part and a 3 m by 3 m part.
6 × 2 = 12 and 3 × 3 = 9, so the area is 21 m².
5
Farida doubles the sides of a square of side 5 cm. Her friend says the area is also doubled. Is the friend right?
No. The area changes from 25 cm² to 10 × 10 = 100 cm², which is 4 times as big.
