Download App

Areas Related to Circles — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsAreas Related to Circles2 Marks
Question
In the following 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 $\pi=\frac{22}{7}$ ]
✓

Answer

In right triangle $A E D$
$A D^2=A E^2+D E^2$
$=(9)^2+(12)^2$
$=81+144$
$=225$
$\therefore AD^2=225$
$\Rightarrow AD=15 cm$
We know that the opposite sides of a rectangle are equal
$A D=B C 15 cm$
Area of the shaded region $=$ Area of rectangle - Area of triangle $A E D+$ Area of semicircle
$=\text{AB}\times\text{BC}-\frac{1}{2}\times\text{AE}\times\text{DE}+\frac{1}{2}\pi\Big(\frac{\text{BC}}{2}\Big)^2$
$=20\times15-\frac{1}{2}\times9\times12+\frac{1}{2}\times\frac{22}{7}\times\big(\frac{15}{2}\big)^2$
$=300-54+88.3982$
$=334.3928\text{cm}^2$
Hence, the area of shaded region is $334.39 \text{cm}^2$

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 "2 Marks Questions" from Areas Related to Circles→Areas Related to Circles — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

In FIg. check whether AD is the bisector of $\angle\text{A}$ of $\triangle\text{ABC}$ in the following.

AB = 6cm, AC = 8cm, BD = 1.5cm and CD = 2cm.
→
The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls balls is $\frac{1}{4}.$ The probability of selecting a blue ball at randome from the same jar is $\frac{1}{3}.$ If the jar contains 10 orange balls, find the total number of balls in the jar.
→
A Wire when bent in the form of an equilateral triangle encloses an area of $121\sqrt{3}\text{cm}^2.$ If the same wire is bent into the form of a circle, what will be the area of the circle? $\Big[\text{Take }\pi=\frac{22}{7}.\Big]$
→
Which of the following sequences are A.P. ? If they are A.P. find the common difference.
$3,3+\sqrt{2}, 3+2 \sqrt{2}, 3+3 \sqrt{2}, \ldots$
→
A number is chosen at random from the number -3, -2, -1, 0, 1, 2, 3. What will be the probability that square of this number is less then or equal to 1?
→
Find the area of $\triangle\text{ABC}$ whose vertices are:
$A(3, 8), B(-4, 2)$ and $C(5, -1)$
→
A share was sold at ₹ 950 market value and brokerage of $0.2 \%$ was paid then how much amount is obtained on selling it?
→
Evaluate:
$=\frac{\sin50^\circ}{\cos40^\circ}+\frac{\text{cosec }40^\circ}{\sec50^\circ}-4 \cos50^\circ\ \text{cosec }40^\circ$
→
From a circular piece of cardboard of radius 3cm two sectors of 90° have been cut off. Find the perimeter of the remaining portion nearest hundredth centimeters $\Big(\text{Take }\pi =\frac{22}{7}\Big). $
→
If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.
→