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Application of Heron’s Formula in Finding the Area of a Quadrilateral

Example 1 :

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

Solution :


If ABCD is a quadrilateral, AB = 9m, BC = 40m, CD = 28m and DA = 15m and ABC = 90°
Area of ABCD = area
Δ ABC + Area Δ ACD
In
Δ ABC, B = 90°
AC2 = AB2 + BC2 = 92 + 402
AC = 41m
Area
Δ ABC =

In
Δ ACD, s =

Area of
Δ ACD = = 126 sq. units
Hence, area of quadrilateral ABCD = 180 + 126 = 306 sq. units. 

 
Example 2 :

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

Solution :


    

In || gm ABCD, AB = CD = 60 m and
AD = BC = 25 m
Diagonal AC = 65 m
In
ΔABC, s == 75 m.
Area of || gm = 2
× Area Δ ABC
= 2
= 2
= 1500 sq. m

 





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