- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# The area of an equilateral triangle ABC is $17320.5\ cm^2$. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see figure). Find the area of the shaded region.

(Use $\pi = 3.14$ and $\sqrt3= 1.73205$).

"

Given:

The area of an equilateral triangle ABC is $17320.5\ cm^2$. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle.

To do:

We have to find the area of the shaded region.

Solution:

Area of the equilateral triangle $ABC = 17320.5\ cm^2$

Let the side of the triangle $ABC$ be $a$

This implies,

Area of $\triangle ABC = \frac{\sqrt3}{4}a^2$

$\frac{\sqrt3}{4}a^2= 17320.5$

$ a^{2} =\frac{17320.5 \times 4}{\sqrt{3}}$

$a^{2}=\frac{17320.5 \times 4}{1.73205}$

$a^{2}=40000$

$a=200 \mathrm{~cm}$

Radius of the circle drawn at each vertex $=\frac{1}{2} \text { (side of the equilateral triangle) }$

$=\frac{1}{2} \times 200$

$=100 \mathrm{~cm}$

Area of the sector formed at each vertex having radius $100 \mathrm{~cm}$ and sector angle $60^{\circ}=3.14 \times \frac{100 \times 100 \times 60^{\circ}}{360^{\circ}}$

$=\frac{3.14 \times 100 \times 100}{6}$

$=\frac{31400}{6}$

Area of all 3 sectors $=\frac{3 \times 31400}{6}$

$=15700 \mathrm{~cm}^{2}$

Therefore,

Area of the shaded portion $=$ Area of the equilateral triangle

$-$ Area of the three sectors formed at each vertex

$= 17320.5 - 15700$

$= 1620.5\ cm^2$

The area of the shaded region is $1620.5\ cm^2$

- Related Questions & Answers
- Area of circle which is inscribed in an equilateral triangle?
- Program to calculate the Area and Perimeter of Incircle of an Equilateral Triangle What is Equilateral Triangle in C?
- Area of circle which is inscribed in equilateral triangle in C Program?
- Program to calculate area of Circumcircle of an Equilateral Triangle
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle in C Program?
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle in C Program?
- Program to calculate area and perimeter of equilateral triangle
- Program to calculate area of Circumcircle of an Equilateral Triangle in C++
- Program to calculate area and perimeter of equilateral triangle in C++
- Area of Reuleaux Triangle?
- Check if a triangle of positive area is possible with the given angles in Python
- C++ program to find the Radius of the incircle of the triangle
- Biggest Reuleaux Triangle inscribed within a Square inscribed in an equilateral triangle?
- Java program to find the area of a triangle
- C Program to check whether the triangle is equilateral, isosceles or scalene
- How to Calculate the Area of a Triangle using Python?