Area & Perimeter of Plane Shapes – JSS1 Mathematics Lesson Note (Third Term)

Perimeter is the distance around the outside boundary of a plane shape, and area is the amount of surface the shape covers.

Behavioural objectives

By the end of the lesson, students should be able to:

1. state what the perimeter and the area of a plane shape are;
2. calculate the perimeter of a rectangle, a square, a triangle, a parallelogram and a circle;
3. calculate the area of a rectangle, a square, a triangle, a parallelogram and a trapezium;
4. change centimetres to metres when solving perimeter problems.

What is a plane shape?

A plane shape is a flat shape that has length and width but no thickness.

• Rectangle: four sides with opposite sides equal and four right angles, as in a classroom floor.
• Square: four equal sides and four right angles, as in a floor tile.
• Triangle: three sides, as in a roof frame seen from the front.
• Parallelogram: four sides with opposite sides equal and parallel.
• Trapezium: four sides with one pair of parallel sides.
• Circle: a round shape, as in a coin or a plate.

What are the units of perimeter and area?

Perimeter is measured in units of length, and area is measured in square units.

• Perimeter units: mm, cm and m.
• Area units: mm², cm² and m².
• Rule: change all measurements to the same unit before you calculate.

What is the perimeter of a plane shape?

The perimeter of a plane shape is the length of its outside boundary, which is the distance around its edges.

What are the formulas for perimeter?

Example 1: perimeter of a rectangle

The length of a rectangular room is 5 m and the width is 4 m. Find the perimeter of the room.

Solution

1. Length = 5 m and width = 4 m.
2. Perimeter = 2(l + w)
3. Perimeter = 2(5 + 4)
4. Perimeter = 2 × 9 = 18 m

Example 2: perimeter of a square

The perimeter of a square is 2580 cm. Find the length of the square in metres.

Solution

1. Change to metres: P = 2580 cm = 25.8 m.
2. P = 4 × length = 4l
3. l = 25.8 ÷ 4
4. l = 6.45 m

Therefore, the length of the square is 6.45 m.

Example 3: perimeter of a triangle

Calculate the perimeter of a triangle with dimensions 4.2 m, 3.6 m and 5.7 m.

Solution

1. Perimeter = sum of the three sides.
2. Perimeter = (4.2 + 3.6 + 5.7) m
3. Perimeter = 13.5 m

Example 4: perimeter of a parallelogram

A parallelogram has sides measuring 200 mm by 150 mm. What is the length of the side of a square that has the same perimeter?

Solution

1. Perimeter of the parallelogram = 2(l + w)
2. Perimeter = 2(200 + 150) mm
3. Perimeter = 2 × 350 = 700 mm
4. The perimeter of the square is also 700 mm, so 4l = 700 mm.
5. Divide both sides by the coefficient of l (that is, 4).
6. l = 700 ÷ 4 = 175 mm

Therefore, the length of the square is 175 mm.

Example 5: perimeter of a circle

Calculate the perimeter of a circle of diameter 14 cm.

• Circumference: the perimeter of a circle.
• Diameter (D): the distance across the circle through the centre.
• Radius (r): the distance from the centre to the edge, so D = 2r.

Solution

Method 1: C = πd

1. C = 22/7 × 14
2. C = 44 cm

Method 2: C = 2πr

1. r = D/2 = 14/2 = 7 cm
2. C = 2 × 22/7 × 7
3. C = 44 cm

What is the area of a plane shape?

The area of a shape is the measure of the amount of surface it covers or occupies.

What are the formulas for area?

• Height: always the straight distance at right angles to the base, not the slanting side.
• Answer unit: write area in square units, such as cm².

Example 1: area of a rectangle

Calculate the area of a rectangular room with dimensions 250 cm by 200 cm.

Solution

1. A = l × b
2. A = 250 × 200 cm²
3. A = 50 000 cm²

Example 2: area of a square

Find the area of a square of sides 14 cm.

Solution

1. A = l × l
2. A = 14 × 14
3. A = 196 cm²

Example 3: area of a triangle

Find the area of a triangle with a base of 10 cm and a perpendicular height of 6 cm.

Solution

1. A = ½ × b × h
2. A = ½ × 10 × 6
3. A = 30 cm²

Example 4: area of a parallelogram

Evaluate the area of a parallelogram with a base of 8 cm and a height of 9 cm.

Solution

1. A = b × h
2. A = 8 × 9
3. A = 72 cm²

Example 5: area of a trapezium

Calculate the area of a trapezium with parallel sides of 10 cm and 18 cm and a height of 12 cm.

Solution

1. Area = ½ (sum of parallel sides) × height
2. Area = ½ (10 + 18) × 12
3. Area = ½ (28) × 12
4. Area = 14 × 12
5. Area = 168 cm²

What is the difference between perimeter and area?

Perimeter measures the distance around a shape, while area measures the surface inside it.

Evaluation

1. What is the perimeter of a plane shape? What is the area of a plane shape?
2. A rectangular room is 6 m long and 3 m wide. Find its perimeter.
3. Find the area of a square of side 9 cm.
4. Find the circumference of a circle of radius 7 cm. (Take π = 22/7.)
5. Find the area of a parallelogram with a base of 10 cm and a height of 5 cm.

Assignment

1. The perimeter of a square is 3200 cm. Find the length of the square in metres.
2. Calculate the perimeter of a triangle with sides 2.5 m, 3.5 m and 4 m.
3. Calculate the area of a trapezium with parallel sides of 6 cm and 14 cm and a height of 10 cm.