# 5th Class Mathematics Area, Perimeter and Volume Area, Perimetre and Volume of Geometrical Figures

Area, Perimetre and Volume of Geometrical Figures

Category : 5th Class

Area, Perimetre and Volume of Geometrical Figures

Perimeter

Perimeter is referred as the length of the boundary line, which surrounds the area occupied by a geometrical shape.

• Example:

Find the perimeter of the following figure.

Solution: Perimeter of the figure =

$4\text{ }cm+3\text{ }cm+4\text{ }cm+2.5\text{ }cm+5\text{ }cm+5\text{ }cm$$=23.50\text{ }cm.$

Perimeter of the Triangles

A triangles has three sides. Perimeter of a triangle is the sum of its all the three sides.

Perimeter of the triangle $ABC=AB+BC+CA$

• Example

Find the perimeter of the following triangle.

Solution: Perimeter of the triangle PQR

$\begin{array}{*{35}{l}} =4\text{ }cm+4.7\text{ }cm+6\text{ }cm \\ =14.7\text{ }cm \\ \end{array}$

Perimeter of the Quadrilateral

Perimeter of a quadrilateral is the sum of the length of its four sides.

In quadrilateral ABCD, perimeter

$=AB+BC+CD+DA$

• Example

Find the perimeter of the following quadrilateral.

Solution: Perimeter of the quadrilateral

$=5\text{ }cm+3\text{ }cm+4\text{ }cm+3\text{ }cm=15\text{ }cm$

Perimeter of Rectangles

Perimeter of a rectangle$=2\text{ (}Length+Breadth)$.

• Example

Find the perimeter of the rectangle whose length is 12 cm and breadth is 8 cm.

Solution: Perimeter of the rectangle

$=2\text{ (12}+8)=40\,\,cm.$

Perimeter of Squares

Perimeter of a square$=4\times side$.

Perimeter of the square ABCD = $=4\times AB$

• Example:

Find the perimeter of the square whose length of one side is 9 cm.

Solution: Perimeter of a square

$=4\times 9\text{ }cm=36\text{ }cm$

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.

Unit of the area is $c{{m}^{2}}$ or ${{m}^{2}}$.

Area of a Triangle

Area of a triangle = $\frac{1}{2}\times base\times height.$

Where base is the one side of a triangle and height is length of line segment drawn $90{}^\circ$on the base of that triangle.

• Example:

Find the area of the triangle whose base is 75 cm and height is 80 cm.

Solution: Area of the triangle

$=\frac{1}{2}\times 75cm\times 80cm=3000c{{m}^{2}}$

Area of a Rectangle

Area of a rectangle = length $\times$ breadth.

Area of the rectangle PQRS $=PQ\times QR.$

• Example:

Find the area of the rectangle whose length is 17 cm and breadth is 15 cm.

Solution: Area of the rectangle

$=17\text{ }cm\times 15\text{ }cm=255\text{ }c{{m}^{2}}$

Area of a Square

Area of a square $=sid{{e}^{2}}=side\times side$

Area of the square PQRS$=PQ\times PQ=P{{Q}^{2}}$

• Example:

Find the area of the square whose length of each side is 21 cm.

Solution: Area of the square

$=21\text{ }cm\times 21\text{ }cm=441\text{ }c{{m}^{2}}$

Volume

In our daily life the number of things is stored in different kinds of container. Holding capacity of a container is called volume.

Volume of a Cuboid

Volume of a cuboid =$length\times breadth\times height=lbh$.

Where, length = AB, breadth = AE and height = BC

Volume of the cuboid ABCDEFG$=AB\times BC\times AE.$

• Example:

Find the volume of the cuboid whose length, breadth and height are 15 cm, 13 cm and 14 cm respectively.

Solution: Volume of the cuboid

$=15\text{ }cm\times 13\text{ }cm\times 14\text{ }cm=2730\text{ }c{{m}^{3}}$

Volume of a Cube

Volume of a cube $=sid{{e}^{3}}=side\times side\times side$

• Example:

Find the volume of the cube whose length is 19 cm.

Solution: Volume of the cube

$=19cm\times 19cm\times 19cm=6859c{{m}^{3}}$

#### Other Topics

##### Notes - Area, Perimetre and Volume of Geometrical Figures

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