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

Area, Perimeter and Volume of Geometrical Figures

Category : 5th Class

Area, Perimeter 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 cm + 3 cm + 4 cm + 2.5 cm+ 5 cm + cm = 23.50.

Perimeter of the Triangle

A triangle 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 = 4 cm + 4.7 cm + 6 cm= 14.7 cm

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 cm + 3 cm + 4 cm + 3 cm = 15 cm

Perimeter of Rectangles

Perimeter of a rectangle = 2 (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 (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 = $4\,\,\times \,\,9$cm = 36 cm

Perimeter of a Circle

Perimeter of a circle = $2\pi r$

Where $\pi$$=\,\frac{22}{7}$ = 3.14 and r = radius of the circle

•      Example

If radius of a circle is 0.35 cm, find the perimeter of the circle.

Solution:

Perimeter the circle$=\,\,2\,\,\times \,\,\frac{22}{7}\,\,\times \,\,0.35\,\,cm$= 2.2 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 $cm_{{}}^{2}$ or$mr_{{}}^{2}$.

Area of a Triangle

Area of a triangle $=\,\,\frac{1}{2}$ 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 $=\,\,\frac{1}{2}\,\,\times \,\,75\,\,cm\,\,\times \,\,80\,\,cm\,\,=\,\,3000\,\,cm_{{}}^{2}$

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 $=\,\,17\,\,cm\,\,\times \,\,15\,\,cm\,\,=\,\,255\,\,cm_{{}}^{2}$

Area of a Square

Area of a square $=\,\,side_{{}}^{2}\,=\,\,side\,\,\times \,\,side$

Area of the square PQRS $=\,\,PQ\,\,\times \,\,PQ\,\,=\,\,PQ_{{}}^{2}.$

•              Example

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

Solution:

Area of the square $=\,\,21\,\,cm\,\,\times \,\,21\,\,cm\,\,=\,\,441\,\,cm_{{}}^{2}$

Area of a Circle

Area of the circle $=\,\,\pi \,\,r_{{}}^{2}$

Where $\pi \,\,=\,\,\frac{22}{7}\,\,=\,\,3.14$

•             Example

Find the area of the circle whose radius is 0.28 cm.

Solution:

Area of a circle$=\,\,\frac{22}{7}\,\,\times \,\,0.28\,\,cm\,\,\times \,\,0.28\,\,cm\,\,=\,\,0.2464\,\,cm_{{}}^{2}$

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 $=\,\,15\,\,cm\,\,\times \,\,13\,\,cm\,\,\times \,\,14\,\,cm\,\,=\,\,2730\,\,cm_{{}}^{2}$

Volume of a Cube

Volume of a cube $=\,\,side_{{}}^{3}\,\,=\,\,side\,\,\times \,\,side\,\,\times \,\,side\,$

•              Example

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

Solution:

Volume of the cube $=\,\,19\,\,cm\,\,\times \,\,19\,\,cm\,\,\times \,\,19\,\,cm\,\,=\,\,6859\,\,cm_{{}}^{3}$

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