5th Class Mathematics Area, Perimeter and Volume Area

Area

Category : 5th Class

Area

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.

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 $\pi {{r}^{2}}$

$=\frac{22}{7}\times 11.9\text{ }cm\text{ }\times 11.9\text{ }cm$

$=445.06\text{ }c{{m}^{2}}$

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