Question

Calculate the area of a quadrilateral $ABCD$ when length of the diagonal $AC=10cm$ and the lengths of perpendiculars from $B$ and $D$ on $AC$ be $5cm$ and $6cm$ respectively.

• A. $75c{m}^2$
• B. $65c{m}^2$
• C. $45c{m}^2$
• D. $55c{m}^2$

Answer 1

Answer: (D)

$55c{m}^2$

$BN=5cmDM=6cm$

Area of quadrilateral $ABCD=$ area of $\Delta ACD+$ area of $\Delta ABC$

$=\frac{1}{2}\times AC\times DM+\frac{1}{2}\times BN\times AC$

$=\frac{1}{2}\times 10\times 6+\frac{1}{2}\times 5\times 10$

$=\frac{1}{2}(60+50)$

$=\frac{1}{2}\times 110$

$=55c{m}^2$