In context to the given figure, analyse the following statements: (i) The area of shaded region GEFCD is 546 cm². (ii) The area of r

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Solution

Q.
In context to the given figure, analyse the following statements:

(i) The area of shaded region GEFCD is $546 c m ² .$

(ii) The area of region (AEG + EBF) is 77 $c m ² .$

(iii) The area of shaded region GEFCD is 469 $c m ² .$

(iv) The area of shaded region (AEG + EBF) is 308 $c m ² .$

Which of the above statements are correct Choose the correct option from the following:

1 (i) and (ii)

2 (iii) and (iv)

3 (i) and (iii)

4 (ii) and (iv)

Ans.
(1)

AGE and FEB are quarter circles with radius $\frac{14}{2} = 7 cm$

Therefore, Area of quarter circles AGE + Area of quarter circle FEB

$= \frac{π (7)^{2}}{4} + \frac{π (7)^{2}}{4} = \frac{π (7)^{2}}{2} = \frac{22}{7} \times \frac{(7)^{2}}{2} = 77 c m^{2} ∴ (i i) is correct Area of upper semi - circle (diameter DC) = \frac{1}{2} \times \frac{π (DC)^{2}}{4} = \frac{22}{7} \times \frac{14 \times 14}{4} \times \frac{1}{2} = 77 {cm}^{2} Area of blue shaded region = Area of rectangle ABCD - Area of region (AEG + FEB) - Area of semicircle with diameter DC = (50 \times 14) - 77 - 77 = 546 cm 2 ∴ (i) is correct$

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