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Question

In quadrilateral ABCD, if AB=7 cm,BC=12 cm,CD=12 cm,DA=9 cm and diagonal AC=15 cm. What is its area>

A
(1017+54)sq cm
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B
(103454)sq cm
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C
Data insufficient
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D
None of these
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Solution

The correct option is B (1017+54)sq cm
R.E.F image
ar(ABCD)=ar(ABC)+ar(ACD)
for Δ(ADC)
Use heron's formula
S=15+12+92=18cm
ar(ABC)=S(Sa)(Sb)(Sc)
ar(ABC)=18×3×6×9=54cm
||ly for Δ(ACB)
S=15+12+72=17
ar(ABC)=17×(1715)(1712)(177)=1017cm2
ar(ABCD)=(1017+54)cm2

1070607_509804_ans_c8a81681c4c540da9601f7a86b6f94b3.png

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