Question

In figure, ABCD is a trapezium with $AB\parallel DC$. AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. Arcs of equal radii 7 cm with centres A, B, C and D have been drawn , then find the area of the shaded region in the figure.

• A. $148c{m}^2$
• B. $196c{m}^2$
• C. $126c{m}^2$
• D. $121c{m}^2$

Answer 1

The correct option is B

$196c{m}^2$

Given: AB = 18 cm, DC = 32 cm, height, (h) = 14 cm and are of radii = 7 cm

Since,$AB\parallel DC$

$\therefore \angle A+\angle D={180}^{\circ }$ And $\angle B+\angle C={180}^{\circ }$

$\therefore$ Area of sector with angle A and D $=\frac{\theta \times \pi r^2}{360}$

$=\frac{{180}^{\circ }}{360}\times \frac{22}{7}\times (7{)}^2$

$=11\times 7=77c{m}^2$

Similarly, area of sector with angle B and C = 77 cm

Now, area of trapezium $=\frac{1}{2}(AB+DC)\times h$

$=\frac{1}{2}(18+32)\times 14=\frac{50}{2}\times 14=350c{m}^2$

$\therefore$ Area of shaded region = Area of trapezium - ( Area of 4 sectors at points A , B, C and D)

$=350-(77+77)=196c{m}^2$

Hence, the required area of shaded region is $196c{m}^2$