In this post we will try to understand about the concept of area and how to calculate it using different formulas. Keep in mind that you have to remember the formulas as it would help us to solve problem of mensuration.

We have tried to explain the concept with illustrations so that it gets easier for you to grasp the concept. Also we have provided some solved problems for your better understanding.

## Concept of Area

### What is Area?

The amount of surface enclosed by a closed figure is called its area

The yellow shaded region enclosed by the figures are the areas but by looking it is not possible to calculate area

**How to calculate area of such irregular figures**

**Step – 1:** Place the figures on a squared paper or graph paper where every square measure 1 cm × 1 cm.

**Step – 2: **Make an outline of the figure.

**Step – 3:** Look at the squares enclosed by the figure. Some of them are completely enclosed, some half, some less than half and some more than half.

**Step – 4:** Count the number of squares (both complete and half, ignore less than half squares) and add them.

- The area of one full square is taken as 1 sq unit. If it is a centimeter square sheet, then area of one full square will be 1 sq cm.
- Ignore portions of the area that are less than half a square.
- If more than half of a square is in a region, just count it as one square.
- If exactly half the square is counted, take its area as ½ sq unit.

The area is the number of centimeter squares that are needed to cover it.

Thus, for figure 1 the area is 6 sq. units and for figure 2 the area is 8 sq. units

**Area of regular shapes**

**Square**

**Area = length of each side x length of each side = s x s**

##### Example

**Q1) Find the area of a square whose side is 6 m.**

**Sol.** Given, length of each side (s) = 6 m

Since, area of square = length of each side (s) x length of each side (s)

= s x s

= 6 x 6 m

= 36 sq.m or 36 m^{2}

**Hence, area of the square whose side is 6 m is 24 m.** A**ns.**

**Q2) Find the side of the square whose area is 64 sq.m.**

**Sol.** Given, area = 64 sq.m

But we know that area of a square = length of each side (s) x length of each side (s)

Therefore, 64 sq.m = s x s

√64 = s

8 m = s

**Hence, the length of side of square whose perimeter is 64 sq.m is 8 m**

#### Rectangle

Area = length of rectangle x breadth of rectangle

= L x B

**Q1) Find the area of a rectangle whose length and breadth are 150 cm and 1 m respectively.**

**Sol.** Given, Length = 150 cm

& Breadth = 1 m = 100 cm

Since, area of the rectangle = length x breadth

= 150 cm x 100 cm

= 15000 sq.cm

**Hence, area of rectangle is 15000 sq.cm. Ans.**

**Q2) The area of a rectangular park is 400m. Find the length the park if breadth is 50 m.**

**Sol.** Given, area of rectangular park = 400 m

& breadth = 50 m

To find – length of rectangular park

Since, area of a rectangle = length + breadth

Putting values,

400 sq.m = length x 50 m

400 sq.m/50 m = length

80 m = length

**Hence, length of rectangular park is 80 m. **

#### Triangle

**Area of triangle if height and base is given**

**If “b” is the base and “h” is the height of the triangle, then****Area = half of product of height and base****Area = ½ x b x h**

**Area of triangle using Heron’s formula**

**If all the sides of the triangle are of different length, then area is calculated using heron’s formula****Area = **√s (s – a) (s – b) (s – c)

Where, s = semi-perimeter = (a + b + c)/2

Question 01 :**Find the area a triangle having height 10 cm and length of base 8 cm.**

**Sol.** Given, height (h) = 10 cm and length of base (b) = 8 cm

Since, area of triangle = ½ x b x h

= ½ x 10 cm x 8 cm

= 40 sq.cm

**Hence, area of triangle is 40 sq.cm **

Question 02:**Find the area a triangle having sides 10 cm, 8 cm and 6 cm**

**Sol.** Given, a = 10 cm, b = 8 cm and c = 6 cm

Since, area of triangle = √s (s – a) (s – b) (s – c)

Where, s = semi-perimeter = (a + b + c)/2

s = (10 + 8 + 6)/2 = 24/2 = 12

Putting values = √12 (12 – 10) (12 – 8) (12 – 6)

= √12 (2) (4) (6)

= √12 (2) (4) (6)

= √576

= 24 sq.cm

**Hence, area of triangle is 24 sq.cm Ans.**

#### Rhombus

Area= length of each side x length of each side

= s x s

**Q1) Find the area of rhombus of side 10 cm.**

**Sol.** Given, side = 10 cm

Since, area of rhombus = length of each side (s) x length of each side (s)

= 10 x 10

= 100 sq.cm

**Hence, area of rhombus is 100 sq.cm. **

#### Parallelogram

**Q) Find the area of a parallelogram whose length and breadth are 15 cm and 10 cm respectively.**

**Sol.** Given, Length = 15 cm

& Breadth = 10 cm

Since, area of the parallelogram = length x breadth

= 15 cm x 10 cm

= 150 sq.cm

**Hence, area of parallelogram is 150 cm. **

** **Circle

Area of circle = πr** ^{2}** units

Where, π = 22/7

Here “r” represents the radius of a circle

**Q) Find the area of a circle having radius = 7 cm.**

**Sol.** Given, radius = 7 cm

Since, Area of circle, A = πr^{2}

A = 22/7 x 7 x 7 = 154 sq.cm

**Hence, area of circle is 154 sq.cm. **

#### Semi-circle

Perimeter or circumference of semi-circle = πr** ^{2}**/2

Where, π = 22/7

**Q) Find the area of a semi-circle having radius = 7 cm.**

**Sol.** Given, radius = 7 cm

Area of semi-circle, A = πr** ^{2}**/2

A = 22/7 x 7 x 7/2

A = 11 x 7 = 77 sq.cm

**Hence, area of semi-circle is 77 sq.cm **