Question

In the given figure ABCD is a trapezium in which AB = 40 m, BC = 15 m, CD = 28 m, AD = 9 m and CE ⊥ AB. Area of trap. ABCD is


(a) 306 m²
(b) 316 m²
(c) 296 m²
(d) 284 m²

Answer 1

(a) 306 m²

In the given figure, AECD is a rectangle.

Length AE = Length CD = 28 m

Now,
$BE=AB-AE=40-28=12\mathrm{m}$

Also,
AD = CE = 9 m
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{trapezium}=\frac{1}{2}\times \mathrm{Sum}\mathrm{of}\mathrm{parallel}\mathrm{sides}\times \mathrm{Distance}\mathrm{between}\mathrm{them} \\ =\frac{1}{2}\times (DC+AB)\times CE \\ =\frac{1}{2}\times (28+40)\times 9 \\ =\frac{1}{2}\times 68\times 9 \\ =306{\mathrm{m}}^2 \end{gathered}$$

In the given figure, if DA is perpendicular to AE, then it can be solved, otherwise it cannot be solved.