Question:
Tick (✓) the correct answer:
In the given figure, AB||DC and DA ⊥ AB. If DC = 7 cm, BC = 10 cm, AB = 13 cm and CL ⊥ AB, the area of trap. ABCD is
(a) 84 cm2
(b) 72 cm2
(c) 80 cm2
(d) 91 cm2.png)
Solution:
(c) $80 \mathrm{~cm}^{2}$
From the given trapezium, we find:
$D C=A L=7 \mathrm{~cm} \quad[$ since $D A \perp A B$ and $C L \perp A B]$
From the right $\Delta$ CBL, we have :
$C L^{2}=C B^{2}-L B^{2}$
$\Rightarrow C L^{2}=(10)^{2}-(6)^{2}$
$\Rightarrow C L^{2}=100-36$
$\Rightarrow C L^{2}=64$
$\Rightarrow C L=\sqrt{64}$
$\Rightarrow C L=8 \mathrm{~cm}$
Area of the trapezium $=\left\{\frac{1}{2} \times(7+13) \times 8\right\} \mathrm{cm}^{2}$
$=\left(\frac{1}{2} \times 20 \times 8\right) \mathrm{cm}^{2}$
$=80 \mathrm{~cm}^{2}$