4th Class Mathematics Area, Perimeter and Volume Area and Perimetre

                                                                Area and Perimetre

Introduction

In the previous chapter we have studied about the shape and size of some geometrical figures. In this chapter we will study about area and perimetre of some close geometrical figures.

Area

Area is referred as the surface occupied by the geometrical shapes

Area of a Triangle

Area of a triangle \[=\frac{1}{2}\times Base\times Height\]

Where base is one side of a triangle and height is the length of altitude drawn from opposite vertex on the given base.

Area of the triangle ABC\[=\frac{1}{2}\times AD\times BC\]

Where BC is the base and AD is the height.

• Example

Find the area of the triangle whose base is 5 cm and height is 8 cm.

Solution:

Area of the triangle \[=\frac{1}{2}\times 5cm\times 8cm=20c{{m}^{2}}\]

Area of a Rectangle

Area of a rectangle \[=Length\times Breadth\]

Area of the rectangle ABCD =\[=AB\times BC\]

• Example

Find the area of the rectangle whose length is 9 cm and width is 7 cm.

Solution:

Area of the rectangle \[=9cm\times 7cm=63c{{m}^{2}}\]

Area of a Square

Area of a square \[=Side\times Side\]

Area of the square ABCD\[=AB\times AB\]

• Example

Find the area of the square whose length of one side is 6 cm.

Solution:

Area of the square ABCD \[=6cm\times 6cm=36c{{m}^{2}}\]

Perimetre

Perimetre is referred as the length of the boundary line which endorsee area.

Perimetre of the Triangles

Perimetre of a triangle = Sum of length of all three sides.

Perimetre of the triangle \[ABC=AB+BC+CA\]

• Example

Find the perimetre of the given figure.

Solution: Perimetre of the figure

\[=6.5\text{ }cm+7\text{ }cm+4\text{ }cm=17.5\text{ }cm\]

Perimetre of a Quadrilateral

The perimetre of a quadrilateral = Sum of the length of all four sides.

Perimetre of the quadrilateral ABCD

\[=AB+BC+CD+DA\]

• Example

Find the perimetre of the quadrilateral whose length are 4 cm, 7 cm, 3 cm and 5.2 cm.

Solution:

Perimetre of the quadrilateral

\[=4\text{ }cm+7\text{ }cm+3\text{ }cm+5.2\text{ }cm=19.2\text{ }cm\]

Perimetre of a Rectangle

Perimetre of a rectangle \[=2\,\,(Length+Breadth)\]

Perimetre of the rectangle ABCD \[=2\,\,(AB+BC)\]

• Example

Find the perimetre of the rectangle whose length and breadth are 9 cm and 8 cm.

Solution:

Perimetre of the rectangle \[=2\text{ (}9\text{ }cm+8\text{ }cm)=34\text{ }cm\]

Perimetre of a Square

Perimetre of a square \[=4\times \]length of one side of the square.

Perimetre of the square ABCD \[=4\times AB\]