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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 $$(10\sqrt {17} + 54)sq\ cm$$
R.E.F image 
$$ ar (ABCD) = ar(ABC)+ar(ACD) $$
for $$ \Delta (ADC) $$
Use heron's formula
$$ S = \dfrac{15+12+9}{2} = 18\,cm $$
$$ ar (ABC) = \sqrt{S(S-a)(S-b)(S-c)} $$
$$ \boxed {ar(ABC) = \sqrt{18\times 3\times 6\times 9} = 54\,cm} $$
||ly for $$\Delta (ACB) $$
$$ S = \dfrac{15+12+7}{2} = 17 $$
$$ \boxed {ar(ABC) = \sqrt{17\times (17-15)(17-12)(17-7)} = 10\sqrt{17}cm^{2}} $$
$$ \Rightarrow \boxed {ar(ABCD) = (10\sqrt{17}+54)cm^{2}} $$ 

1070607_509804_ans_c8a81681c4c540da9601f7a86b6f94b3.png

Mathematics

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