Question

Find the area of the shaded region in the adjacent figure, take π = 3.14.

Answer 1

Step-by-step explanation:

We can find the answer of the shaded region by subtracting area of rectangle from the area of circle.

$area \: of \: circle \: = {\pi \: r}^{2} \\ area \: of \: rectangle = l \times b$

Using Pythagoras theorem we can find diameter of circle,

$(12)^{2} + (5)^{2} = {d}^{2}$

where d is diameter,

$144 + 25 = {d}^{2} \\ 169 = {d}^{2} \\ d = \sqrt{169} \\ d = 13$

Now r=d/2,

So radius r = 6.5

$area \: of \: circle \: = \pi \times (6.5) ^{2} \\ area \: of \: circle = 3.14 \times 42.25 \\ area \: of \: circle \: = 132.665 {cm}^{2}$

$area \: of \: rectangle \: = 12 \times 5 = 60 {cm}^{2}$

So area of shaded region = area of circle- area of rectangle,

area of shaded region=132.665-60

Area of shaded region = 72.665cm^2

Answer 2

We can find the answer of the shaded region by subtracting area of rectangle from the area of circle.

Using Pythagoras theorem we can find diameter of circle,

where d is diameter,

Now r=d/2,

So radius r = 6.5

So area of shaded region = area of circle- area of rectangle,

area of shaded region=132.665-60

Area of shaded region = 72.665cm^2