Area and Perimetre

**Category : **4th Class

** 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 \[=4\times AB\]

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