Question

The area of quadrilateral ABCD in the given figure is

(a) $57c{m}^2$

(b) $108c{m}^2$

(c) $114c{m}^2$

(d) $195c{m}^2$

Answer 1

(c)114 cm 2
ar (quad. ABCD) = ar (∆ ABC) + ar (∆ ACD)
In right angle triangle ACD, we have:
AC^ = 17^2 - 8^2 = 225 = 15 cm
In right angle triangle ABC, we have:
BC^2 = 15^2 - 9^2 = 144 = 12 cm
Now, we have the following:
ar(∆ ABC) = 1/2 × 12 × 9 = 54 cm 2
ar(∆ ADC) = 1/2 × 15 × 8 = 60 cm 2
ar(quad. ABCD) =​ 54 + 60 = 114 cm