Innings2
Create New Account

Sign in to Innings2

or

New Account     Reset Password     

Chapter 9: Area of Plane Figures

    Introduction

    Area of a Trapezium

    Area of a Quadrilateral

    Area of a Rhombus

    Surveying the Field

    Area of a Polygon

    Area of a Circle

    Area of a Circular Path or Area of a Ring

    Length of the Arc

    Area of Sector

    Exercise 9.1

    Exercise 9.2

    What We Have Discussed?

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

Powered by Innings 2

Reset Progress

This will delete your progress and chat data for all chapters in this course, and cannot be undone!

Glossary

Select one of the keywords on the left…

Chapter 9: Area of Plane Figures > Area of a Circle

Area of a Circle

But how do we actually calculate the area of a circle? Let’s try the same technique we used for finding the area of quadrilaterals: we cut the shape into multiple different parts, and then rearrange them into a different shape we already know the area of (e.g. a rectangle or a triangle).

The only difference is that, because circles are curved, we have to use some approximations:

rπr

Here you can see a circle divided into ${toWord(n1)} wedges. Move the slider, to line up the wedges in one row.

If we increase the number of wedges to ${n1}, this shape starts to look more and more like a .

The height of the rectangle is equal to the of the circle. The width of the rectangle is equal to of the circle. (Notice how half of the wedges face down and half of them face up.)

Therefore the total area of the rectangle is approximately A=πr2.
r2πr

Here you can see a circle divided into ${toWord(n)} rings. Like before, you can move the slider to “uncurl” the rings.

If we increase the number of rings to ${n2}, this shape starts to look more and more like a .

The height of the triangle is equal to the of the circle. The base of the triangle is equal to of the circle. Therefore the total area of the triangle is approximately

A=12base×height=πr2