In the given figure, from a rectangular region A B C D with A B=2… - Vidyadip

Question

In the given figure, from a rectangular region $A B C D$ with $A B=20 cm$, a right triangle $A E D$ with $A E=9 cm$ and $D E=12 cm$, is cut off. On the other end, taking $BC$ as diameter, a semicircle is added on outside the region. Find the area of the shaded region. [Use $\pi=3.14$ ]

✓

Answer

$ \text { In right-angled } \triangle \mathrm{AED},$
$ \mathrm{AD}^2=\mathrm{DE}^2+\mathrm{AE}^2=12^2+9^2=144+81=225$
$ \Rightarrow \mathrm{AD}=\sqrt{225}=15 \mathrm{~cm}$
$ \text { Now, Area of } \triangle \mathrm{AED}=\frac{1}{2} \times \mathrm{DE} \times \mathrm{AE}=\frac{1}{2} \times 12 \times 9=54 \mathrm{~cm}^2$
$ \text { Length of rectangle } \mathrm{ABCD}=\mathrm{AB}=20 \mathrm{~cm}$
$ \text { Breadth of rectangle } \mathrm{ABCD}=\mathrm{AD}=15 \mathrm{~cm}$
$ \therefore \text { Area of rectangle } \mathrm{ABCD}=\mathrm{AB} \times \mathrm{BC}=20 \times 15=300 \mathrm{~cm}^2$
$ \text { Area of semi-circle }=\frac{1}{2} \pi \times\left(\frac{15}{2}\right)^2=\left\{\frac{1}{2} \times 3.14 \times 7.5 \times 7.5\right\} \mathrm{cm}^2=88.3125 \mathrm{~cm}^2$
$ \text { Thus, Area of rectangle } \mathrm{ABCD}+\text { Area of semi-circle }- \text { Area of } \triangle \mathrm{AED}$
$ =300+88.31-54$
$ =334.31 \mathrm{~cm}^2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Questions" from Area of Circle, Sector and Segment→Area of Circle, Sector and Segment — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

Find the mean of each of the following frequency distributions:

Classes	$25-29$	$30-34$	$35-39$	$40-44$	$45-49$	$50-54$	$55-59$
Frequency	$14$	$22$	$16$	$6$	$5$	$3$	$4$

One side of a rectangle is $12\ cm$ long and its diagonal measures $37\ cm$. Find the other side and the area of the rectangle.

A straight highway leads to the foot of a tower. A man standing on the top of the tower observes a car at an angle of depression of $30^\circ , $which is approaching the foot of the tower with a uniform speed. Six secounds later, the angle of depression of the car is fo d to be $60^\circ $. Find the time taken by the car to reach the foot of the tower form this point.

What is the sum of first n terms of the $AP$ $a, 3a, 5a, ....$

For the following statments state whether true $(T)$ or false$(F):$
The length of the line segment joining the midpoint of any two sides of a triangle is equal to half the length of the third side.

If $10$ times the $10^{\text {th }}$ term of an $AP$ is equal to $15$ times the $15^{\text {th }}$ term, show that its $25^{\text {th }}$ term is zero.

In the given pairs of triangles, find which pair of triangles are similar. State the similarity criterior and write the similarity relation in symbolic from.

Find the roots of the following equation, if they exist, by applying the quadratic formula:
$x^2+5 x-\left(a^2+a-6\right)=0$

All integers between $100$ and $550$ which are not divisible by $9.$

Solve for $x$ and $y$:
$\frac{2}{(3\text{x}+\text{2y)}}+\frac{3}{(3\text{x}-\text{2y)}}=\frac{17}{5},$
$\frac{5}{(3\text{x}+\text{2y)}}+\frac{1}{(3\text{x}-\text{2y)}}=2$