Question

in figure ABCD is a parallelogram a semi circle with Centre O and the diameter a v has been drawn and it passes through D if ab is equals to 12 cm and OD is perpendicular to a b then find the area of shaded region​

Answer 1

Answer:

please mark as brain list...

Answer 2

Answer is 33.48 $cm^2$

Step-by-step explanation:

As in Figure,

• Area of Parallelogram ABCD = $AB \times DO$ ($Base \times Height/Altitude$)

= $12 \times 6$ (As DO = OB = $\frac {AB}{2}$ [Radius])

= $72\ cm^2$

• Area of Semi-circle = $\frac {\pi r^2}{2}$

= $3.14 \times 6 \times 6 \times \frac {1}{2}$

= $\frac {314}{100} \times 36 \times \frac {1}{2}$

= $\frac {5652}{100}$

= 56.52 $cm^2$

• Area of ΔAOD = $\frac {1}{2} \times AO \times DO$

= $\frac {1}{2} \times 6 \times 6$

= 18 $cm^2$

• Required Shaded Area = Area of Parallelogram - Area of Semi-Circle + Area of ΔAOD

= 72 - 56.52 + 18

= 90 - 56.52

= 33.48 $cm^2$