Download App

Areas Related to Circles — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsAreas Related to Circles2 Marks
Question
In the following figure, from a rectangular region $ABCD$ with $AB = 20\ cm$, a right triangle $AED$ with $AE = 9\ cm$ and $DE = 12\ cm$, 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.$\Big[\text{Use }\pi=\frac{22}{7}\Big]$
✓

Answer

In right triangle $AED$
$ A D^2=A E^2+D E^2 $
$ =(9)^2+(12)^2 $
$= 81 + 144$
$= 225$
$\therefore\text{AD}^2=225$
$\Rightarrow\text{AD}=15\text{cm}$
We know that the opposite sides of a rectangle are equal
$AD = BC\  15\ cm$
Area of the shaded region = Area of rectangle − Area of triangle $AED$ + 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→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

The area of a sector is one-twelfth that of the complete circle. Find the angle of the sector.
→
Find the sum of the APs: $\frac{1}{{15}},\frac{1}{{12}},\frac{1}{{10}},.....$ to $11$ terms.
→
Prove that $(\text{cosec A}-\cot\text{A})^2=\frac{(1-\cos\text{A})}{(1+\cos\text{A})}.$
→
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is $20$ years. Four years ago, the product of their ages in years was $48$.
→
A solid metallic sphere of diameter $21\ cm$ is melted and recast into small cones of diameter $3.5\ cm$ and height $3\ cm$ each. Find the number of cones so formed.
→
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = ax^2+ bx + c,$ then evaluate:
$\frac{1}{\alpha}+\frac{1}{\beta}-2\alpha\beta$
→
Very-Short-Answer Question:
Write the zeros of the polynomial $x^2- x - 6$
→
In the given figure, $\angle$ ACB = 90° and CD $\perp$ AB. prove that $\frac { B C ^ { 2 } } { A C ^ { 2 } } = \frac { B D } { A D }$.
→
An arc of length $20\pi\text{ cm}$ subtends an angle of $144^\circ$ at the centre of a circle. Find the radius of the circle.
→
In the following figures, you find who triangles. Indicate whether the triangles are similar. Give reasons in support of your answer.​​​​​​​​
→