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In a quadrilateral the sides are 9, 40, 28, 15 units and the angle between the first two sides is a right angle. The area of the quadrilateral is.

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106 sq. units

206 sq. units

306 sq. units

406 sq. units

answer is C.

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Detailed Solution

https://www.vedantu.com/question-sets/c3846751-7667-41ea-a89b-cf22c75eb9cb8853797380397386342.png

From the given, ∠DAB is a right angle triangle.
Using Pythagoras theorem,

∴ D B^{2} = D A^{2} + A B^{2}

\Rightarrow D B^{2} = 9^{2} + 40^{2}

Taking square root on both sides we get,

\Rightarrow DB = \sqrt{81 + 1600}

Hence,
DB = 41 unit
Let us consider the △DAB,
We have

s = \frac{9 + 40 + 41}{2}

\Rightarrow s = \frac{90}{2}

Hence,
s = 45 units
Since, area of

△ DAB = A 1 = \sqrt{s (s - a) (s - b) (s - c)}

Let substitute the values,
⇒

\sqrt{45 (45 - 9) (45 - 40) (45 - 41)}

⇒45×36×5×4
⇒180 sq. unit
Let us consider the △DCB,
We have,

s = \frac{28 + 15 + 41}{2}

\Rightarrow s = \frac{84}{2}

Hence,
⇒ s= 42 units

Area of △ DCB = A 2 = \sqrt{s (s - a) (s - b) (s - c)} \Rightarrow \sqrt{42 \times (42 - 38) \times (42 - 15) \times (42 - 41)} sq . units

\Rightarrow \sqrt{42 \times 14 \times 27 \times 1}

⇒126sq. units
Hence, area of quadrilateral = A1 + A2
⇒(180+126)
Hence, area of quadrilateral =306 sq. units.
So, option 3 is correct.

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