Question

Two sides of a plot measure 32 m and 24 m and the angle between them 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 (in m²)?

(a) 768 

(b) 534 

(c) 696.5 

(d) 684

Answer 1

(d)  684 m²

In right angle Δ ADC, 

AC² = AD² + DC²

⇒ AC = \(\sqrt{24^2 + 32^2}\) = \(\sqrt{576+1024}\) = \(\sqrt{1600}\) = 40 m

∴ Area of the plot = Area of Δ ADC + Area of Δ ABC 

For Δ ABC, S = \(\frac{25+25+40}{2}\) m = 45 m

∴ Required area = \(\frac12\) x 24m x 32m + \(\sqrt{45(45-25)(45-25)(45-40)}\) m²

= 384 m² + \(\sqrt{45\times20\times20\times5}\) m²

= 384 m² + 300 m² = 684 m².