Question

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

• A. $768m^2$
• B. $534m^2$
• C. $696.5m^2$
• D. $684m^2$

Answer 1

Answer: (D)

$684m^2$

$arABCD=ar△ADC+ar△ABC$

$ar△ADC=\frac{1}{2}\times 24\times 32=384m^2$

Now, $AC=\sqrt{{AD}^2+{DC}^2}$

$=\sqrt{{24}^2+{32}^2}=\sqrt{1600}=40m$

$\therefore ar△ABC=\sqrt{s(s-a)(s-b)(s-c)},S=\frac{40+25+25}{2}=45m$

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

$=\sqrt{45\times 5\times 20\times 20}=15\times 20=300m^2$

$\therefore ar.ABCD=384+300=684m^2$