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Vinay K30

Guest

Area of shaded region

ABCD is a rectangle with AB = 14cm and BC = 7 cm. AFB and CED are semi circles on AB and CD as diameters as in figure*? *Find the area of the shaded region

FluxBB bbcode test]http://www.mathisfunforum.com/img/test.png[/img

I am unable to paste the picture. Pls help

Srikantan

Member

From: Tanjore

Registered: 2016-06-04

Posts: 42

Re: Area of shaded region

https://drive.google.com/file/d/0B4Y0zkk0dzBKVWp0RzVMeXd6ejNRenBkaDd4N29SUWhHamJn/view?usp=drivesdk

Srikantan

Member

From: Tanjore

Registered: 2016-06-04

Posts: 42

Re: Area of shaded region

Image in above link. My friend had posted question

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Area of shaded region

hi Vinay and Srikantan

Interesting question.  Thanks for posting it. I have made an accurate diagram using 'Sketchpad' and labelled some regions.  I shall also use the same letters to represent the area of that region.

Note first that the triangle made by 2D is equilateral so we know its angles.

You will have to use pi in the calculations so exact accuracy is not possible.  Therefore you might as well use 22/7 for pi as this will allow some simplification of the calculations.

(1) Calculate the area of the semi circle =  2B + 4C + 4D

(2) Calculate the area of the sector 4D + 2C (has angle 120 and is therefore 1/3 the whole circle)

(3) Calculate the area of the segment C by calculating the sector 2D + C and subtracting the area of the equilateral triangle 2D.

(4) Using these three answers you can calculate 2B and hence answer the question.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Srikantan

Member

From: Tanjore

Registered: 2016-06-04

Posts: 42

Re: Area of shaded region

Thanks a ton

Srikantan

Member

From: Tanjore

Registered: 2016-06-04

Posts: 42

Re: Area of shaded region

Sorry i am not clear on step 2. Can you explain little.in detail

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Area of shaded region

I have edited the diagram in my post to show the sector I mean.  It has radii of 7, and an angle of 120.  It consists of the regions D + D + D + D + C + C

Hope that helps.

An alternative calculation would be to find the segment above the 7,7,120 triangle, double it and subtract from (1).

In terms of B, C and D it comes to the same thing.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob