Question

Find the area of a quadrilateral field, whose diagonal is 30 m and perpendiculars drawn to it from the opposite vertices are 14 m and 12m​

Answer 1

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Length of diagonal of a quadrilateral =30cm

⇒  Length of  two perpendicular lines =19cm and 11cm.

Area of a quadrilateral =21×onediaginal×sumofthetwoperpendicularlines

                                      =21×30×(19+11)

                                      =21×30×30

                                     =15×30

                                     =450cm2.

Answer 2

Given :-

• One Diagonal of quadrilateral = 30m
• Perpendiculars = 14m and 12m

To Find :-

• Area of Quadrilateral .

Solution :-

⇒ Area = ½ × Diagonal × Sum of Perpendicular

⇒ Area of Quadrilateral = ½ × 30 × 14 + 12

⇒ Area of Quadrilateral = 15 × 14 + 12

⇒ Area of Quadrilateral = 15 × 26

⇒ Area of Quadrilateral = 390m²

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So, Area of Quadrilateral is 390m²

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★ Additional Info :

• A Quadrilateral having exactly one pair of parallel sides is called Trapezium.
• A Quadrilateral with each pair of opposite sides parallel is called a Parallelogram.

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