## Definition

**Definition**

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its **Area**.

Now, imagine your square is made up of smaller unit squares. The area of a figure is counted as the number of unit squares required to cover the overall surface area of that particular 2-D shape. Square cms, square feet, square inches, square meters, etc., are some of the common units of area measurement.To find out the area of the square figures drawn below, draw unit squares of 1-centimeter sides. Thus, the shape will be measured in **cm²**, also known as square centimeters.

Here, the area of the shapes below will be measured in square meters (m²) and square inches (in²).

How to calculate the area if there are also half unit squares in the grid?

To understand that, let us take one more example:

**Step 1**: Count the full squares.

There are 18 full squares.

**Step 2:** Count the half squares.

On counting, we see that there are 6 half squares.

**Step 3:** 1 full square $= 1$ square unit

So, 18 full square $= 18$ square units

1 half square $= \frac{1}{2}$ square unit

6 half squares $= 3$ square units

Total area $= 18 + 3 = 21$ square units.

**Origin of the Term: Area**

The term ‘area’ originated from Latin, meaning ‘a plain piece of empty land’. It also means ‘a particular amount of space contained within a set of boundaries’.

**More about Area**

Look at the carpet in your home. To buy a carpet that fits the floor, we need to know its area. Or the carpet will be bigger or smaller than the space! Some other instances when we need to know the area are while fitting tiles on the floor, painting the wall or sticking wallpaper to it, or finding out the total number of tiles needed to build a swimming pool.

## Formulas for Calculating Area

We are surrounded by so many 2-D shapes: circle, triangle, square, rectangle, parallelogram, and trapezium. You can draw all of these shapes on your paper. Every shape is different and unique, so its area is also calculated differently. To find the area, first, identify the shape. Then, use the appropriate formula from the list given below to find its area.

## Areas of Composite Figures

Every plane figure cannot be classified as a simple rectangle, square, triangle, or typical shape in real life. Some figures are made up of more than one simple 2-D shape. Let us join a rectangle and a semicircle.

These shapes formed by the combination of two or more simple shapes are called “**composite figures**” or **“composite shapes**”.

For finding the area of a composite figure, we must find the sum of the area of all the shapes in it. So, the area of the shape we just drew will be the area of the rectangle,* **l$\times$ **b** *plus* *half* *the area of the circle, ½ x *πr²*, where l and b are length and breadth of the rectangle and r is the radius of the semicircle.

If we draw a semi – circle below a triangle, we get the composite shape:

The area of such a composite figure will be calculated by adding the area of the triangle and the area of the semicircle.

Area of the a composite figure =($\frac{1}{2}\times b\times h) (\frac{1}{2}+𝜋r^2$)

where r is the radius of the semicircle and b and h are the base and height of the triangle respectively.

**Real-life Applications**

Here are a few ways in which you can apply the knowledge of the area of figures in your daily life.

- We can find the area of a gifting paper to check whether it will be able to cover a box or not.
- We can find the area of a square or circle to find the area of the signal board.

## Solved Examples

**A circle has a diameter of 20 cm. Find out the area of this circle.**

Ans: For the circle, *d* = 20 cm.

Radius, *r* = $\frac{d}{2}$ = 10 cm

Therefore, *A* = π*r*²

= 3.14$\times 10\times 10$ = 314 cm$^{2}$

Area of the given circle is 314 $cm^{2}$.

**The height of a triangle is 10 cm and the base is 20 cm. What is the area of this triangle?**

Ans: Area of the triangle = $\frac{1}{2}\times b\times h$

= $\frac{1}{2}\times 20\times 10 = 100 cm^{2}$

Therefore, the area of the given triangle is 100 $cm^{2}$.

**The width of a rectangle is half of its length. The width is measured to be 10 cm. What is the area of the rectangle?**

Ans: For the rectangle, *w* = 10 cm and* l *= (10 $\times$ 2) = 20 cm.

Area of the rectangle, i.e., A = l $\times$ w

A = 20 $\times$ 10 = 200 cm$^{2}$

Therefore, the area of the given rectangle is 200 cm$^{2}$.

**Example 4: What is the area of the following figure?**

Solution: Full square $= 1$ square unit

So, 14 full square $= 14$ square units

1 half square $= \frac{1}{2}$ square units

5 half squares $= 2.5$ square units

Total area $= 14 + 2.5 = 16.5$ square units.

## Practice Problems

## Area

### The side of a square is 7 cm. What is the area of this square?

Area of the square = side $\times$ side

**A = 7 $\times$ 7 = 49 cm$^{2}$**

### The height of a triangle is 25 cm and the base is 50 cm. What is the area of the triangle?

Area of the triangle = $\frac{1}{2}\times b\times h = \frac{1}{2}\times 50\times 25$ = 625 cm$^{2}$

### What is the area of a circle that has a radius of 4 cm?

^{2}

Area of the circle = 𝜋r$^{2}$ = 3.14$\times 4\times 4$ = 50.27 cm$^{2}$

### The base of a parallelogram is 50 cm and the perpendicular height is 20 cm. What is the area of this parallelogram?

Area of the parallelogram = b$\times$ h = 50$\times$ 20 = 1000 cm$^{2}$

**Conclusion**

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## Frequently Asked Questions

**How do the perimeter and the area of a shape differ?**

Perimeter and area are related to the 2-D geometry of shapes. Perimeter is the total length of the outline around the shape, while area is the total space inside the shape.

**Why is the area measured in square units but perimeter is not?**

Area is a measure of the number of unit squares that fit in a 2-D shape, so it is expressed in square units. Perimeter is the measure of the length of the outline of the shape and is expressed in linear units.

**What is the importance of the concept of area for learning?**

The knowledge of the area of a shape gives students a clear understanding of the total space covered within the boundary of that shape. This concept has many real-life applications, like finding the carpet area of a room, finding the total size of the wall that needs to be painted, etc.

**How is the area of an irregular shape measured?**

Divide the irregular shape into unit squares and calculate the total number of unit squares. If a few unit squares are not occupied entirely, approximate to 0 or 1 for each.