The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in orde

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The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively and the angle between the first two sides is a right angle. Find its area.

Options:

A .

18 + 24 \sqrt{2} c m^{2}

B .

18 + 24 \sqrt{6} c m^{2}

C .

36 + 24 \sqrt{2} c m^{2}

D .

36 + 24 \sqrt{6} c m^{2}

Answer: Option B
:
B

The Sides Of A Quadrilateral ABCD Are 6 Cm, 8 Cm, 12 Cm And ...

Area of

△ A B C = \frac{1}{2} \times base \times h e i g h t

= \frac{1}{2} \times 6 \times 8

= 24 c m^{2}

Diagonal AC =

\sqrt{B C^{2} + A B^{2}} = 10 c m

For

△ A C D,

s = \frac{10 + 12 + 14}{2} = 18

Area

= \sqrt{s (s - a) (s - b) (s - c)}

= \sqrt{18 (18 - 10) (18 - 12) (18 - 14)}

= \sqrt{18 \times 8 \times 6 \times 4}

= 24 \sqrt{6} c m^{2}

∴

area of quadrilateral

= 18 + 24 \sqrt{6} c m^{2}

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