Find the area of the shaded region in Fig. 4, if $ABCD$ is a rectangle with sides $8\ cm$ and $6\ cm$ and $O$ is the center of circle. $( Take\ \pi= 3.14)$ "
Given: Sides of the rectangle $=8\ cm$ and $6\ cm$. $O$ is the center of circle.
To do: To find the area of the shaded region.
Solution:
Here, diagonal $AC=$diameter of the circle.
$\vartriangle ABC$, is a right triangle.
Using Pythagoras theorem
$\Rightarrow AC^{2}=AB^{2}+BC^{2}$
$\Rightarrow AC^{2}=8^{2}+6^{2}$
$\Rightarrow AC^{2}=64+36=100$
$\Rightarrow AC=\sqrt{100}=10\ cm$
Radius of the circle, $OC= \frac{diameter(AC)}{2}$
$ =\frac{10}{2}$
$ =5\ cm$
Area of the circle $=\pi r^{2}=3.14\times (5)^{2}=78.5\ cm^{2}$
Area of the rectangle $=8\times6=48\ cm^{2} $
Area of the shaded region $=$Area of the circle$-$Area of rectangle
$=78.5-48$
$=30.5\ cm^{2}$
Therefore, The area of shaded region is $30.5\ cm^{2}$.
Related Articles Find the area of the shaded region, if $PQ=24 cm, PR=7 cm$, and O is the center of the circle."\n
In figure, O is the centre of a circle such that diameter $AB=13\ cm$ and $AC=12\ cm$. $BC$ is joined. Find the area of the shaded region. $( Take\ \pi \ =\ 3.14)$"\n
Find the area of the shaded region in the below figure, if \( A C=24 \mathrm{~cm}, B C=10 \mathrm{~cm} \) and \( O \) is the centre of the circle. (Use \( \pi=3.14) \)"\n
In fig. 3, a square OABC is inscribed in a quadrant OPBQ of a circle. If $OA\ =\ 20\ cm$, find the area of the shaded region $( Use\ \pi =\ 3.14)$."\n
In fig OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with center O, then find the area of the shaded region.$\left[ Use\ \pi =\frac{22}{7}\right]$"\n
The circumference of a circle is $31.4\ cm$. Find the radius and the area of the circle? $(Take\ \pi=3.14)$
In Fig 4, a circle is inscribed in an equilateral triangle $\vartriangle ABC$ of side $12\ cm$. Find the radius of inscribed circle and the area of the shaded region. [$Use\ \pi =3.14\ and\ \sqrt{3} =1.73$]."\n
In the below figure, an equilateral triangle \( A B C \) of side \( 6 \mathrm{~cm} \) has been inscribed in a circle. Find the area of the shaded region. (Take \( \pi=3.14) \)"\n
In the figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If $OD = 2\ cm$, find the area of the shaded region."
Find the area of the shaded region in the given figure, if $PQ = 24\ cm, PR = 7\ cm$ and $O$ is the centre of the circle."
In the below figure, \( O A C B \) is a quadrant of a circle with centre \( O \) and radius \( 3.5 \mathrm{~cm} \). If \( O D=2 \mathrm{~cm} \), find the area of the shaded region."\n
In Fig.5. PSR, RTQ and PAQ are three semicircles of diameters 10 cm, 3 cm and 7 cm respectively. Find the perimeter of the shaded region. [Use $\pi = 3.14$]"\n
Rectangle ABCD is formed in a circle as shown in the figure. If $AE =8 cm$ and $AD=5 cm$, find the perimeter of the rectangle."\n
From the circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. (Take $\pi=3.14$)
From a circular sheet of radius $4\ cm$, a circle of radius $3\ cm$ is removed. Find the area of the remaining sheet. $(Take\ \pi=3.14)$
Kickstart Your Career
Get certified by completing the course
Get Started