Question

The area of quadrilateral ABCD in the given figure is
(a) 57 cm²
(b) 108 cm²
(c) 114 cm²
(d) 195 cm²

Answer 1

(c)114 cm²

ar (quad. ABCD) = ar (∆ ABC) + ar (∆ ACD)
In right angle triangle ACD, we have:
AC = $\sqrt{\left({17}^2-8^2\right)}=\sqrt{225}=15\mathrm{cm}$
In right angle triangle ABC, we have:
BC = $\sqrt{\left({15}^2-9^2\right)}=\sqrt{144}=12\mathrm{cm}$
Now, we have the following:
ar(∆ABC) = $\frac{1}{2}$ × 12 × 9 = 54 cm²
ar(∆ADC) = $\frac{1}{2}$ × 15 × 8 = 60 cm²
ar(quad. ABCD) =​ 54 + 60 = 114 cm²