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What will be the area of quadrilateral ABCD in the given figure?

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57cm2

108cm2

114cm2

None of these

answer is C.

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Detailed Solution

It is given that,
Question Image

We have to find the area of quadrilateral ABCD.
The area of the triangle, that is

12 × b a s e × h e i g h t

In ΔABC, calculating the value of AC using Pythagoras Theorem,

A B 2 = A C 2 + B C 2 ⇒ A C 2 = A B 2 − B C 2 ⇒ A C 2 = 172 − 82 ⇒ A C = 225 ⇒ A C = 15 c m

In ΔACD, calculating the value of CD using Pythagoras Theorem,

A C 2 = A D 2 + C D 2 ⇒ C D 2 = A C 2 − A D 2 ⇒ C D 2 = 152 − 92 ⇒ C D = 144 ⇒ C D = 12 c m

Area (quad. ABCD)= Area (∆ABC)+ Area (∆ACD)
Here, Area (quad. ABCD)= Area (∆ABC)+ Area (∆ACD)

= 12 A C × B C + 12 A D × C D = 1215 × 8 + 129 × 12 = 60 + 54 = 114 c m 2

So, area(quad. ABCD) =

114 c m 2

Therefore, option 3 is correct.

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