turkey-yks 2011 Q37

turkey-yks · Other · ygs Radians, Arc Length and Sector Area
$$|\widehat{AD}| = a \text{ units}$$ $$|\widehat{BC}| = b \text{ units}$$ $$|DC| = c \text{ units}$$
The OAD and OBC circular sectors with center O are given above.
Accordingly, the area of the shaded region is equal to which of the following in terms of $a, b$ and $c$?
A) $\frac{(a + b) \cdot c}{2}$ B) $\frac{(b - a) \cdot c}{2}$ C) $\frac{2(a + b)}{c}$ D) $\frac{2(b - a)}{c}$ E) $\frac{a \cdot b \cdot c}{2}$
$$|\widehat{AD}| = a \text{ units}$$
$$|\widehat{BC}| = b \text{ units}$$
$$|DC| = c \text{ units}$$

The OAD and OBC circular sectors with center O are given above.

Accordingly, the area of the shaded region is equal to which of the following in terms of $a, b$ and $c$?

A) $\frac{(a + b) \cdot c}{2}$
B) $\frac{(b - a) \cdot c}{2}$
C) $\frac{2(a + b)}{c}$
D) $\frac{2(b - a)}{c}$
E) $\frac{a \cdot b \cdot c}{2}$