Q11 of 99 Page 269

In a quadrilateral ABCD, AB = 5 meter, BC = 12 meter, CD = 14 meter, DA = 15 meter and ∠ABC = 90°, let us write by calculating the area of quadrilateral shape of field.

Given, a quadrilateral ABCD in which,

AB = 5m


BC = 12m


CD = 14m


And DA = 15m


∠ABC = 90



In ∆ABC,


⟹ AC2=AB2+BC2


⟹ AC2=52+122


⟹ AC2=169


⟹ AC=13m


∴ area of ∆ABC = ×5×12


= 30 sq. m


And diagonal AC=13m


Semi perimeter of ∆ADC, S =


S = 21m


Hence area of ∆ADC = sq. m


Area ∆ABC = 84 sq. m


∴ total area of the quadrilateral = area of (∆ABC +∆ADC)


= 30 + 84


= 114 sq. m


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