Question

Find the area of the coloured region.

Answer 1

Hint: We will find the area of a rectangle $ ABCD $ . Thereafter we will find the area of the quadrant. Further, we will find the area of colored regions. By using the formula of:
Area of rectangle $ = length \times breadth $
Area of quadrant $ = \dfrac{1}{4}\pi {r^2},r = radius $ .

Complete step-by-step answer:
Now, $ ABCD $ ; is a rectangle and $ DEF $ is a quadrant.
So, length of rectangle \[\left( l \right) = 9cm\]
And breadth of a rectangle $ (b) = 10cm $
Then by using the formula of the area of the rectangle.
Area of rectangles $ = l \times b $
Now, we will put the value of $ l\,\,and\,\,b $ in the formula, we have
Area of rectangle $ = 10 \times b $
Area of rectangle $ = 9 \times 10 $
Area of rectangle $ = 90c{m^2} $
Now, we will see that the unshaded part is the in the form of quadrant
So, radius $ DE = 4cm $
Then, by using the formula of area of quadrant, We will get
 $ \Rightarrow $ Area of quadrant $ = \dfrac{1}{4} \times \pi \times {(4)^2} $
 $ \Rightarrow $ Area of quadrant $ = \dfrac{1}{4} \times \pi \times 4 \times 4 $
 $ \Rightarrow $ Area of quadrant $ = \dfrac{1}{4} \times \dfrac{{22}}{7} \times 4 \times 4 $
 $ \Rightarrow $ Area of quadrant $ = \dfrac{{22}}{7} \times 4 $
 $ \Rightarrow $ Area of quadrant $ = \dfrac{{88}}{7} $
 $ \Rightarrow $ Area of quadrant $ = 12.57c{m^2} $
Then we will find area of the colored region:
 $ = $ area of rectangle ABCD- area of quadrant
 $
   = 90c{m^2} - 12.57c{m^2} \\
   = 77.43c{m^2} \;
  $
Hence, the area of coloured region is $ 77.43cm $

Note: Students must know that in order to find the area of the coloured part, we will subtract the area of the unshaded part with the area of the whole part to get the answer.