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
B
(103454)sq cm
C
Data insufficient
D
None of these

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 $$\Delta (ACB)$$$$S = \dfrac{15+12+7}{2} = 17$$$$\boxed {ar(ABC) = \sqrt{17\times (17-15)(17-12)(17-7)} = 10\sqrt{17}cm^{2}}$$$$\Rightarrow \boxed {ar(ABCD) = (10\sqrt{17}+54)cm^{2}}$$ Mathematics

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