Question

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

• A. $682sq.m$
• B. $684sq.m$
• C. $686sq.m$
• D. $688sq.m$

Answer 1

The correct option is B $684sq.m$

In $△ABC,\angle ABC={90}^o$

$\Rightarrow$ $(AC{)}^2=(AB{)}^2+(BC{)}^2$

$\Rightarrow$ $(AC{)}^2=(24{)}^2+(32{)}^2$

$\Rightarrow$ $(AC{)}^2=576+1024$

$\Rightarrow$ $(AC{)}^2=1600$

$\therefore$ $AC=40m$

$\Rightarrow$ Area of $△ABC=\frac{1}{2}\times BC\times AB$

$=\frac{1}{2}\times 32\times 24$

$=384m^2$

$\Rightarrow$ Semi-perimeter of $△ADC\left(s\right)=\frac{25+25+40}{2}=\frac{90}{2}=45m$

$\Rightarrow$ Area of $△ADC=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{\left(45\right(45-25\left)\right(45-25\left)\right(45-40)}$

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

$=\sqrt{90000}$

$=300m^2$

$\therefore$ Area of plot $=(384+300)m^2=684m^2$