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**Area of Quadrilateral**

Area is the region covered by a closed plane figure.
Quadrilateral is a closed plane figure bounded by four sides.

**Area of quadrilaterals**can be measured by using different formula for different types of regular shaped quadrilaterals. They are as given below:

*Area of rectangle = l × b**, where l = length of rectangle and b = breadth of rectangle*

*Area of square = l*^{2}or ½ d^{2}*, where l = length of square and d = diagonal*

*Area of parallelogram = b × h**, where b = base and h = height*

*Area of rhombus = ½ × d*_{1}× d_{2}*, where d*

_{1}and d_{2}are two diagonals

*Area of kite = ½ × d*_{1}× d_{2}*, where d*

_{1}and d_{2}are two diagonals

*Area of trapezium = ½ × h × (l*_{1}+ l_{2})*, where h = height and l*

_{1}and l_{2}are two parallel lines

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**Area of a irregular quadrilateral **

Area of irregular or any shaped quadrilateral can be
obtained in terms of its one diagonal and two perpendiculars drawn from the
opposite vertices to the diagonal.

In the given figure, PQRS is a quadrilateral in which QS is a diagonal. PA and RB are perpendiculars drawn from the vertex P and R respectively to the
diagonal QS. Suppose, QS = d, PA = h

_{1}and RB = h_{2}.
We can write:

Area of quadrilateral PQRS = Area of ΔPQS + Area of ΔRQS

= ½ QS × PA + ½ QS × RB

= ½ d ×h

_{1}+ ½ d × h_{2}
= ½ d (h

_{1}+ h_{2})**∴ Area of quadrilateral = ½ d (h**where, d is a diagonal, h

_{1}+ h_{2})_{1}and h

_{2}are the perpendiculars drawn from the opposite vertices to the diagonal d.

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*Workout Example*

*Workout Example*

*Example 1: Find the area of the given quadrilateral.*

*Solution: From the figure,*

*Length of diagonal (d) = 14cm*

*h1 = 5cm*

*h2 = 4cm*

*Area of quadrilateral = ½ d (h*_{1}+ h_{2})

*= ½ × 14 (5 + 4)*

*= ½ × 14 × 9*

*= 63 cm*^{2}

*You can comment your questions or problems regarding the area of quadrilaterals here.*

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