Question

A land ABCD is in the shape of a Quadrilateral has $\angle C=90,AB=9m,BC=12m,CD=5m$ and $AD=8m$. How much area does it occupy?

• A. $30+6\sqrt{5}{m}^2$
• B. $30+6\sqrt{35}{m}^2$
• C. $30+6\sqrt{125}{m}^2$
• D. None of the above

Answer 1

The correct option is B $30+6\sqrt{35}{m}^2$

$BD=\sqrt{{12}^2+5^2}=\sqrt{144+25}=\sqrt{169}=13m$
Area of $△BDC=\frac{1}{2}\times 12\times 5m^2=6\times 5=30m^2$
Area of \triangle ABD
$S=\frac{9+8+13}{2}=\frac{17+13}{2}=\frac{30}{2}=15$
$=\sqrt{15\times (15-9)(15-8)(15-13)}$
$=\sqrt{15\times 6\times 7\times 2}$
$=\sqrt{3\times 5\times 3\times 2\times 7\times 2}$
$=3\times 2\sqrt{35}=6\sqrt{35}$
Total area $=30+6\sqrt{35}{m}^2$