# Application of Heronâ€™s Formula in Finding the Area of a Quadrilateral

Find the area of a quadrilateral whose sides are 9m, 40m, 28m and 15m units and the angle between the first two sides is 90Â°.

If ABCD is a quadrilateral, AB = 9m, BC = 40m, CD = 28m and DA = 15m and âˆ ABC = 90Â°

Area of ABCD = area Î” ABC + Area Î” ACD

In Î” ABC, âˆ B = 90Â°

âˆ´ AC^{2 }= AB^{2 }+ BC^{2 }= 9^{2 }+ 40^{2}

âˆ´ AC = 41m

Area Î” ABC =

In Î” ACD, s =

Area of Î” ACD = = 126 sq. units

Hence, area of quadrilateral ABCD = 180 + 126 = 306 sq. units.Â

The parallel sides of a parallelogram are 60 mÂ and 25 m and one of the diagonals is 65 m.Â Find the area of the || gm, if the distanceÂ between the parallel sides is 60 m

Â Â Â Â

In || gm ABCD, AB = CD = 60 m and

AD = BC = 25 m

Diagonal AC = 65 m

In Î”ABC, s == 75 m.

Area of || gm = 2 Ã— Area Î” ABC

= 2

= 2

= 1500 sq. m

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