Question

The area of a kite, whose longest diagonal is 20 cm and the perpendicular distance of the opposite vertices from the diagonal is 6.5 cm, is equal to

• A. $165c{m}^2$
• B. $65c{m}^2$
• C. $130c{m}^2$
• D. $145c{m}^2$

Answer 1

The correct option is C $130c{m}^2$


Let ABCD be a kite such that AB = BC, AD = DC and AD > AB.
Since length of the longest diagonal is 20 cm.
$\therefore$ BD = 20 cm
Also, the perpendicular distance from A on BD is 6.5 cm and diagonals of kite intersect at right angles.
$\therefore$ Area of kite ABCD = $\frac{1}{2}\times AC\times BD$
$=\frac{1}{2}\times 13\times 20$
($\therefore AC=2\times 6.5=13cm$)
$=130c{m}^2$
Hence, the correct answer is option (c).