Math Problem : J.9 Area of shadow area in a circle

In a figure, AB and CD are vertical.

AE = 24 cm, BE = 6 cm, CE = 18 cm, DE = 8 cm.

The area of a circle is 785 cm2

Find the sum of the area of a shadow area.




















Answer
302.5 cm2

Solution
As shown in Fig. 1, the auxiliary line of HI and GF is drawn to be that AB = HI and CD = GF.
EJ =24 - 6 =18cm. EL =18 - 8 = 10cm.


The area of rectangle EJKL is 18 × 10 =180cm2

If equivalence transfer of the part of a shadow area is carried out as shown in Fig. 1, the area of a shadow area and the area of a red portion will become equal.

Therefore, since the area of a shadow area is 1/2 of the remaining area after the area of the rectangle EJKL being subtracted from the area of a circle, the area of a shadow area is (785 - 180) × 12 = 302.5cm2