A plane figure bounded by four line segments is called a quadrilateral.

**Application of Heronâ€™s Formula in Finding Areas
of Quadrilaterals**

A plane figure
bounded by four line segments is called a quadrilateral.

Let *ABCD*
be a quadrilateral. To find the area of a quadrilateral, we divide the quadrilateral
into two triangular parts and use Heronâ€™s formula to calculate the area of the triangular
parts.

In Fig 7.7,

Area of quadrilateral
*ABCD* = Area of triangle *ABC* + Area of triangle *ACD*

**Example 7.3**

A farmer
has a field in the shape of a rhombus. The perimeter of the field is 400*m*
and one of its diagonal is 120*m*. He wants to divide the field into two equal
parts to grow two different types of vegetables. Find the area of the field.

*Solution*

Let *ABCD*
be the rhombus.

Its perimeter
= 4 Ã— side = 400 *m*

Therefore,
each side of the rhombus = 100 *m*

Given the
length of the diagonal AC = 120 *m*

In âˆ†*ABC,* let *a* =100 *m, b* =100 *m,
c* =120 *m*

*s* = (a
+* b *+* c*) / 2 = (100 +100 +120) / 2 = 160* m *

Area of Î”ABC = âˆš [160(160 âˆ’100)(160 âˆ’100)(160 âˆ’120)]

= âˆš [160Ã—60Ã—60Ã—40]

= âˆš [40Ã—2Ã—2Ã—60Ã—60Ã—40]

= 40 Ã—
2 Ã—
60 =
4800*m*^{2}

Therefore,
Area of the field *ABCD* = 2 Ã— Area of ABC = 2 Ã— 4800 = 9600 *m*^{2}

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9th Maths : UNIT 7 : Mensuration : Application of Heronâ€™s Formula in Finding Areas of Quadrilaterals |

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