Question

find the area of the shaded region.​

Answer 1

Answer:

To Find :-

(i) Diameter of the Circle

(ii) Area Of Circle

(iii) Area of Rectangle

(i) Join any of the Diagonal of the Rectangle,

Since, all angles are 90° each,

We Apply the Pythagorean Theorem,

(Diagonal)² = 5² + 12² = 25 + 144 = 169

Diagonal = √169 = 13, Now, you'll notice that the Diagonal is actually the Diameter.

=> DIAMETER = 13m => Radius = 13/2m

(ii) Area Of Circle = πr² = 22/7 × 13/2 × 13/2

=> Area of the Circle = 132.8 m²

(iii) Area Of the Rectangle = l × b

=> 12 × 5 = 60 m²

Now Area Of The Shaded Portion = Area Of the Circle - Area of the Rectangle

=> 132.8 - 60 = 72.8m²

Area Of the Shaded Portion = 72.8 m²....

Answer 2

Here’s the diagram on the basis of which I have solved this question.

We have to find the area of the shaded region.
On examining the figure we can conclude that for solving this problem one must have a basic understanding of circles and a bit of mensuration as well.

Now for the solution:
We know that the diameter of a circle sub tends an angle of 90 degrees to the arc of the circle. We can approach the problem from here:
When we join either AC or BD (for this solution let us take AC)
It is subtending and angle of 90 degrees to the arc of the circle.
Hence, we can conclude that AC is the diameter of the circle.

AC is also the diagonal of rectangle ABCD hence by applying Pythagoras theorem in triangle ACB:
AC^2=AB^2+CB^2
=> AC^2=(12)^2+(5)^2
=> AC^2=169
=> on taking sqrt both sides
=>AC=13m
Hence diameter of the circle is 13m
Now the radius of the circle will be
13/2=6.5m

Now for the area of the shaded region is equal to the area of the circle-area of rectangle
:

π r^2-(12*5)
=> π*(6.5)^2-(12*5)
=> (π*42.25)-(12*5)
=>132.8-60. (Approx)
=>72.8 sq.m

Don’t forget the units.
So the area of the shaded region is 72.8 sq.m
I hope it helps :)