Question

Find the area of a field which is in shape of a parallelogram with sides 12 cm and 14 cm and one of the diagonal of length 18 cm.

• A. $16\sqrt{110}$ $c{m}^2$
• B. $18\sqrt{11}$ $c{m}^2$
• C. $8\sqrt{10}$ $c{m}^2$
• D. $6\sqrt{11}$ $c{m}^2$

Answer 1

The correct option is A $16\sqrt{110}$ $c{m}^2$

Solution:

To find:

$ar\left(llgmABCD\right)=?$

Solution;

$ar\left(△ABD\right)=\sqrt{s(s-a)(s-b)(s-c)}$

here, $a=12,b=14,c=18$

$s=\frac{12+14+18}{2}=22$

$ar\left(△ABD\right)=\sqrt{22(22-12)(22-14)(22-18)}c{m}^2$

$=\sqrt{22\times 10\times 8\times 4}c{m}^2$

$=\sqrt{7040}c{m}^2$

$=8\sqrt{110}c{m}^2$

Now,

$ar\left(llgmABCD\right)=2\times ar\left(△ABD\right)$

$=2\times 8\sqrt{110}$

$=16\sqrt{110}c{m}^2$

Hence, A is the correct answer.