Question

Find the area of the shaded region in the adjacent figure, take π = 3.14
(a) 75 cm2
(b) 72 cm2
(c) 70 cm2
(d) none of these​

Answer 1

Answer:

area of rectangle = l×b

=5×12=60cm

are of circle =πr² - arra of rectangle

=60-5= 75cm²

Answer 2

Option D : The area of the shaded part is $72.665cm^{2}$.

( If rounded to its lower integer, the area is 72 i.e. Option B )

Step 1 : Finding the Radius of the given circle

The diagonal of the rectangle ABCD inside the given circle acts as the diameter of the circle. The inside figure is a rectangle with right angles, so we can apply Pythagorean Theorem as :

                    $(AC)^{2} =(AD)^{2} +(CD)^{2} \\(AC)^{2} =(12)^{2} +(5)^{2} \\(AC)^{2} =144 +25\\ (AC)^{2} =169\\AC = 13cm$

Thus, the diameter of the circle is : AC = 13 cm

So, the radius of the circle can be calculated as :

                   $r = d/2\\r = 13/2\\r = 6.5cm$

Step 2 : Finding the Area of the Circle in the figure

The radius of circle 'r' is 6.5 cm. So, the calculated area is :

              $A_{c} = \pi r^{2} \\A_{c} = 3.14 * (6.5)^{2} \\A_{c} = 132.665 cm^{2}$

Step 3 : Finding the Area of the inscribed Rectangle

The length and breadth of the rectangle inside are 12cm and 5 cm respectively. So, the calculated area is :

              $A_{r} = l * b\\A_{r} = 12 * 5\\A_{r} = 60 cm^{2}$

Step 4 : Finding the Shaded Area

The shaded area is the area of the circle with the area of the rectangle removed from it.

             $A = A_{c} - A_{r} \\A = 132.665 - 60\\A = 72.665 cm^{2}$

Hence, the area of the shaded part is $72.665cm^{2}$.

To learn more about Shaded Area, visit

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