Plane Shapes 3

Plane Shapes

These include shapes like Rectangles, Squares, Circles, etc.

Squares

These have all the sides equal.

Perimeter of a Square

This is the total distance round a square. Since all the sides of a square are equal, and it has four sides, if its length is taken to be L, then the perimeter will be;

P = L+ L+ L+ L

P = 4L

Where P = Perimeter, and L = Length

Example

If the length of a square is 6cm, calculate its Perimeter.

Solution

L = 6cm

P = 4L

P = 4 X 6

= 24cm

Classwork

1. Calculate the perimeter of a square of length 10cm
2. The perimeter of a square is 36cm. Calculate its length.

Area of a Square

The area of a square is given by the formular

A = L²

Where A = Area

L = Length

Example

Calculate the area of a square of length 10cm

Solution

L = 10cm

A = L²

A – 10²

A =100cm²

Classwork

1. Given a square of length 12cm. Calculate its area
2. If the area of a square is 625m². Find its length.

Rectangles

This has the opposites equal.

Perimeter of a Rectangle

P = L+ L +B+ B

P = 2L + 2B

P = 2(L + B)

Example

A rectangle has length 5cm and breadth 7cm. Calculate its perimeter.

Solution

L = 5cm

B = 7cm

P = 2(L + B)

P = 2(5 + 7)

P = 2(12)

= 24cm

Classwork

1. Calculate the perimeter of a rectangle of length 12cm and breadth 15cm.
2. A rectangle has perimeter 20cm and length 5cm. Calculate its breadth

Area of  Rectangle

The area of a rectangle is given by the formular

A = L x B

Where A = area

L = length

B = breadth

Example

The length of a rectangle is 6m and its breadth is 9m. Calculate its area.

Solution

L = 6m

B = 9m

A = L x B

A = 6m x 9m

A = 54m²

Classwork

The length of a rectangle is 17cm and its breadth is 18cm. Calculate its area

Circles         

These are round figures. The Diameter of a circle is a line that divides it into two equal halves. Half of a diameter is called a Radius.

Thus, radius, r = d/2.

Circumference of a Circle

The Circumference, C of a circle is given by;

C = 2πr

Where π is a constant taken as 22/7 or 3.142

r = radius

Example

The radius of a circle is 14m. Calculate its circumference (take π = 22/7)

Solution

r = 14m

π = 22/7

C = 2πr

C = 2 x 22/7 x 14

C =  88m

Classwork

1.  The radius of a circle is 14/11 cm. Calculate its circumference.
2. The circumference of a circle is 10cm. Calculate its radius. (take π = 22/7)

Area of a Circle

The area of a circle is given by

A = πr²

Where A – area

π= 22/7

r = radius

Example

The radius of a circle is 14m. Calculate its area. (take π = 22/7)

Solution

r = 14m

π= 22/7

A = πr²

A = 22/7 x 14²

=22/7 x 196

= 616m²

Classwork

The diameter of a circle is 14cm. Calculate its area. (take π = 22/7)