Area

**Category : **5th Class

All the geometrical shapes occupies some space. The occupied space by a geometrical shape is called area of that geometrical shape.

Shaded part in the above figures represent area.

** Area of a Triangle**

Area of a triangle \[=\frac{1}{2}\times \] base x height.

**Height**

In a triangle, the length of the perpendicular which is drawn from vertex to the opposite side is called height of the triangle.

**Base**

In a triangle, the length of the side of the triangle on which perpendicular is drown is called base.

Area of a triangle \[=\frac{1}{2}\times \] base \[\times \] height

In triangle ABC

Height = CD and base = AB

Area of the triangle \[ABC=\times AB\times CD.\]

**Find the area of the following figure:**

**Explanation**

Area of a triangle \[=\frac{1}{2}\times \] base \[\times \]height

In triangle PQR

Area of the triangle \[\text{PQR=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ QR }\!\!\times\!\!\text{ PS=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ 4cm }\!\!\times\!\!\text{ 7cm14c}{{\text{m}}^{\text{2}}}\]

**Area of a Rectangle**

Area of a rectangle = length \[\times \] breadth.

**Length**

The longer side of a rectangle is called length of the rectangle.

**Breadth**

The shorter side of a rectangle is called breadth of the rectangle.

In the rectangle PQRS

Length of rectangle = Longer side PQ = RS = 7 cm

Breadth of the rectangle = Shorter side

QR = SP = 5 cm

Area of the rectangle PQRS = Length \[\times \] Breadth

= PQ \[\times \] QR.

**Find the area of the following figure:**

In rectangle ABCD

Length = AB = 6 cm

Breadth = BC = 4 cm

Thus area of the rectangle 3 \[\text{ABCD=AB }\!\!\times\!\!\text{ BC=6 cm }\!\!\times\!\!\text{ 4 cm=24 c}{{\text{m}}^{\text{2}}}\text{.}\]

**Area of a Square**

Area of a square\[~=\text{ }sid{{e}^{2}}.\]

In the square PQRS PQ=QR=RS=SP Area of the square \[PQRS\text{ }=\text{ }PQ\text{ }\times \text{ }PQ\] \[=P{{Q}^{2}}.\]

** Find the area of the following figure:**

In square ABCD

AB = BC = CD = DA = 5 cm

Area of the square \[\text{ABCD }=\text{ A}{{\text{B}}^{\text{2}}}\]

\[{{(5cm)}^{2}}=25c{{m}^{2}}\]

**Area of a Circle**

Area of the circle \[=\pi {{r}^{2}}\]

To find the area of a circle, square of the radius is multiplied by the constant \[\pi .\]

**Find the area of the circle whose radius is 11.9 cm. **

**Solution:**

Area of a circle \[\pi {{r}^{2}}\]

\[=\frac{22}{7}\times 11.9\text{ }cm\text{ }\times 11.9\text{ }cm\]

\[=445.06\text{ }c{{m}^{2}}\]

*play_arrow*Area and Perimeter*play_arrow*Introduction*play_arrow*Perimeter*play_arrow*Area*play_arrow*Volume*play_arrow*Area, Perimeter and Volume of Geometrical Figures*play_arrow*Notes - Area, Perimetre and Volume of Geometrical Figures

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