Area

You must have encountered the word area many times in your life. The area is of great importance in day-to-day life. To design the house, to build the roads, to find the flow of water knowing about the concept of the area is very important. The use of the area is not limited to daily use. It is even used in different sciences like Physics. The area of any shape is the space enclosed by the sides of that shape. It gives the number of planes covered by the sides. This is the definition of area for a 2-D shape. In the case of 3-D shapes, the surface area forms a border of that shape.

What Is Area?

The area of any shape gives information about the space covered by that space. Different shapes have different areas. To find the areas we need to make use of different formulas. The International System of Units (SI) unit of area of any shape is sq.m. An alternate way to find the area of any shape is by dividing the plane into small squares of unit areas. Then count the number of squares coming inside the border of the shape.

Area Of Different Shapes

• What is the area of the square?

A square is a shape which has four congruent sides. The area of the square is the plane enclosed by these four sides. To find the area of the square we need to use the formula of the area of the square.

Let the length of the side of a square be denoted by “a”.

The formula for the area of the square is given as follows:

Area = \left ( side \right )^{2} \\

Area = \left ( a \right )^2

• What is the area of a triangle?

Triangle is a figure having three sides. The length of the sides varies for different types of triangles. For example, for an equilateral triangle, all the sides have the same length. For an isosceles triangle, the length of two sides is the same.

To find the area of a triangle you need the value of the height and base of a triangle. The height of the triangle is perpendicular drawn from the vertex to the opposite base.

The formula for the area of a triangle is

Area = \frac{1}{2} \ast base * height

• What is the area of a rectangle?

The rectangle is a shape having opposite sides congruent. The adjacent sides of a rectangle make an angle of 90° with each other.

The longest side of a rectangle is called the length and the shorter side is called the breadth of a rectangle.

The formula for the area of a rectangle can be given as:

Area = length \ast breadth

• What is the area of a parallelogram?

A parallelogram is a shape having an interior opposite angle equal. But the adjacent sides can have different angles between them. The opposite angles/sides of the parallelogram are said to be congruent.

Let us denote the longest side by 'l' and the smallest side by 'b'.

The formula for the area of a parallelogram is as follows:

Area = base \ast height

• What is the area of a rhombus?

A rhombus is a shape having all sides equal. The opposite angles of a rhombus are said to be congruent. The adjacent sides do not necessarily intersect at 90°.

The find the area of a rhombus we need the value of height and breadth.

The formula for the area of a rhombus is as follows:

Area = base \ast height

• What is the area of a circle?

The circle is a shape having no corners. You need a radius to draw the circle. A radius is the distance from the centre to any point on the circle.

Let 'r' be the value of the radius of the circle then the formula of the area of a circle is given as follows:

Area = \pi \left ( r \right )^{2}

• What is an area of trapezium?

A trapezium is a quadrilateral having one pair of parallel sides.

To find the area of the trapezium we need the height and the length of the two parallel sides

Let 'a' and 'b' be the length of the parallel sides and 'h' be the height of the trapezium. The formula for the area of the trapezium is as follows:

Area = \frac{1}{2} \ast\left ( a +b\right ) \ast h

Examples:

1. Find the area of the semicircle having a diameter of 6 units.

Ans: If the diameter of a semicircle is 6 units, the radius of the semicircle is 3 units. A semicircle has half that of a circle having the same radius. Hence the formula of the area of the semicircle is

Area =\frac{\pi\left ( r \right )^{2}}{2} \\

\\

Area =\frac{\pi\left ( 3 \right )^{2}}{2} \\

\\

Area =\frac{\pi\left ( 9 \right )}{2} \\

\\

Area = 4.5 \pi sq. units

2. What is the area of a triangle having a base of 4 cm and a height of 0.07m?

Ans: Before finding the area we must have equal units to do the operation.

1m = 100cm

So, 0.07m = 7cm

The formula for the area of a triangle is

Area = \frac{1}{2} \ast base * height \\

\\

Area = \frac{1}{2} \ast 4 * 7 \\

\\

Area = 14 sq. cm

3. What is the area of a rectangle having the value of length 5cm and perimeter 20cm?

Ans: The formula for the perimeter of a rectangle is

Perimeter = 2(length + breadth) \\

20 = 2(5 + breadth) \\

10 = 5 + breadth \\

breadth = 5

The formula for the area of a rectangle is

Area = length * breadth \\

Area = 5 * 5 \\

Area = 25 sq. cm

4. What is the area of a square having a diagonal of 6 cm?

Ans: The relation between the sides of the diagonal square and its side can be given using Pythagoras' theorem.

\left ( diagonal \right )^{2}=\left ( side \right )^{2} + \left ( side \right )^{2} \\

\left ( diagonal \right )^{2}=2\left ( side\right )^{2} \\

\left ( 6\right )^{2}=2\left ( a \right )^{2} \\

18 = a^{2} \\

a = 3{\sqrt{2}} \ cm

The area of the square is :

Area = (side) ^ {2} \\

Area = (3 {\sqrt{2}})^{2} \\

Area = 18 \ sq. cm

5. Find the area of a square having side of 4 m

Ans: The area of the square is

Area = (side)^{2} \\

Area = (4)^{2} \\

Area = 16 sq.m

Frequently Asked Questions

1. What is the relation between a square and a rhombus

Square is this special case of a rhombus. Every square can be categorized as a rhombus. The reverse of the above statement is not possible.

2. What is the relation between a parallelogram and a rectangle?

The rectangle comes under a special case of a parallelogram.

3. What is the angle between the diagonals of a rhombus?

The diagonals of a rhombus intersect at 90°. Hence, the angle is 90°.

4. What is the area of a semicircle?

The area of a semi-circle is \frac{1}{4} times that of a circle. i.e A= \frac{1}{4}\times (\pi r^2) where ‘r’ is the radius of the circle.