Question

Two sides of a plot measure $32m$ and $24m$ and the angle between them a perfect right angle. The other two sides measure $25m$ each and the other three angles are not right angles. What is the area of the plot? (in $m^2$)

• A. $768$
• B. $534$
• C. $696.5$
• D. $684$

Answer 1

The correct option is D $684$

In right angle $\Delta$ ADC,

$A{C}^2=A{D}^2+D{C}^2$ ....By Pythagoras theorem

$\Rightarrow AC=\sqrt{{24}^2+{32}^2}-\sqrt{576+1024}=\sqrt{1600}$ $=40m$

For $\Delta ABC$,

$s=\frac{25+25+40}{2}=45m$

$\therefore$ Area of the plot $=$ Area of $\Delta ADC+$ Area of $\Delta ABC$

$=\frac{1}{2}\times 24\times 32+$ $+\sqrt{45(45-25)(45-25)(45-40)}$

$=384+\sqrt{45\times 20\times 20\times 5}$

$=384+300$

$=684m^2$