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Hint: Area of a rectangle can be given by relation length $\times $ breadth and area of circle is given as $\pi {{r}^{2}}$ where r is radius and value of $\pi $ is $\dfrac{22}{7}$. Now, find the remaining area by calculating the difference of the areas of rectangle and semi-circle.

Complete step-by-step answer:

Here, we have a rectangle (paper) ABCD where sides AB = 22cm and BC = 14cm, and we have to determine the area of portion remaining after cutting a semi-circular portion with BC as a diameter. Hence, diagram can be given as

Here O is the center of the semi-circle and mid-point of BC as well.

Hence, radius of semicircle BC is 7cm, i.e., $\left( \dfrac{14}{2} \right)$.

Now, we can get the area of the remaining portion of the rectangle by subtracting the area of the whole rectangle by the area of the semi-circle.

Now, we know

$\begin{align}

& \text{area of rectangle = length }\!\!\times\!\!\text{ breadth} \\

& \text{area of circle = }\pi {{\text{r}}^{2}} \\

\end{align}$

Where r = radius, $\pi =\dfrac{22}{7}$

Hence, area of semicircle $=\dfrac{\pi {{r}^{2}}}{2}$

So, we can get area of remaining part from the given diagram as

Remaining area = $AB\times BC-\dfrac{\pi {{r}^{2}}}{2}$

$=22\times 14-\dfrac{22}{7}\times \dfrac{1}{2}\times {{\left( 7 \right)}^{2}}$

$\begin{align}

& =308-11\times 7 \\

& =308-77 \\

& =231c{{m}^{2}} \\

\end{align}$

Hence, the area of the remaining part can be given as 231 sq. cm.

So, option (B) is the correct answer.

Note:

One may get confused between the formula of area and circumference of a circle. So, one may go wrong while using the area of the circle as $2\pi r$. Hence, be clear with the formula of areas of standard shapes.

One may get confused with the center of the semicircle that is the midpoint of BC. Itâ€™s because BC is the diameter of a semi-circle and the midpoint of diameter is center.

Complete step-by-step answer:

Here, we have a rectangle (paper) ABCD where sides AB = 22cm and BC = 14cm, and we have to determine the area of portion remaining after cutting a semi-circular portion with BC as a diameter. Hence, diagram can be given as

Here O is the center of the semi-circle and mid-point of BC as well.

Hence, radius of semicircle BC is 7cm, i.e., $\left( \dfrac{14}{2} \right)$.

Now, we can get the area of the remaining portion of the rectangle by subtracting the area of the whole rectangle by the area of the semi-circle.

Now, we know

$\begin{align}

& \text{area of rectangle = length }\!\!\times\!\!\text{ breadth} \\

& \text{area of circle = }\pi {{\text{r}}^{2}} \\

\end{align}$

Where r = radius, $\pi =\dfrac{22}{7}$

Hence, area of semicircle $=\dfrac{\pi {{r}^{2}}}{2}$

So, we can get area of remaining part from the given diagram as

Remaining area = $AB\times BC-\dfrac{\pi {{r}^{2}}}{2}$

$=22\times 14-\dfrac{22}{7}\times \dfrac{1}{2}\times {{\left( 7 \right)}^{2}}$

$\begin{align}

& =308-11\times 7 \\

& =308-77 \\

& =231c{{m}^{2}} \\

\end{align}$

Hence, the area of the remaining part can be given as 231 sq. cm.

So, option (B) is the correct answer.

Note:

One may get confused between the formula of area and circumference of a circle. So, one may go wrong while using the area of the circle as $2\pi r$. Hence, be clear with the formula of areas of standard shapes.

One may get confused with the center of the semicircle that is the midpoint of BC. Itâ€™s because BC is the diameter of a semi-circle and the midpoint of diameter is center.

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