Area & Perimeter of Plane Shapes JSS1 Mathematics Lesson Note

 AREA AND PERIMETER OF PLANE SHAPES

PERIMETER: The perimeter of a plane shape is the length of its outside boundary. This means the distance around its edges.

Examples 

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

Solution

The length of the room is 5 m.

The width of the room is 4 m.

Perimeter = 2(l+w) 

Perimeter = 2(5+4)

Perimeter = 2(9) = 2×9 = 18m

The perimeter of a square is 2580 cm.  

Find the length of the square in meters.

Solution:

P= 2580cm = 25.8m

P= 4 x length = 4l

L = 25.8/4

L = 6.45m

Therefore, the length of the square = 6.45m

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

Solution:

Perimeter = (4.2 + 3.6 + 5.7) meters

Perimeter = 13.5m

A parallelogram has sides measuring 200mm by 150mm. what would be the length of the side of a square having the same perimeter?

Solution

Length of  parallelogram = 200mm

The width of the parallelogram = 150mm

Perimeter = 2( L + w)

Perimeter = 2(200 + 150) mm

Perimeter = 2 x 350 = 700mm

But

Perimeter of the square = 4 x length = 4L

4L = 700mm

Divide both sides by the coefficient of l 

L = 700/4 = 175

Therefore the length of the square = 175mm

Calculate the perimeter of a circle of diameter 14cm.

NOTE: The perimeter of a circle is called circumference and the diameter (D) is twice the radius (r). thus D = 2r

Solution:

Method 1: circumference = πd

C=πd

C = 22/7 x 14

C = 44cm

Method 2: ∁ =2πr

R = D/2 = 14/2 = 7cm

C = 2 x 22/7 x 7

C= 44cm

AREA: The area of shapes is the measure of the amount of surface it covers or occupies.

Examples :

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

Solution: A=l x b

              A = (250 x 200) square cm

              A =50 000 cm square.

Find the area of a square of sides 14cm.

Solution: A=l x l

                 A = 14 x 14

                A = 196 cm square

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

Solution:

A=b x h 

A = 8 X 9

A = 72 cm square

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

Solution:

Area = 1/2  (sum of parallel sides)x height 

Area = ½ (10 + 18) x 12

Area = ½ (28) x 12

Area = 14 x 12

Area = 168 cm square.