Area of polygon excluding circles

Let there be a $n$ -sided regular polygon ( $n \geq 6$ ) of side length $a$ . Circles are drawn taking each of the vertices as centre and radius $a$ . Find the area of the polygon that is not included in any circle.

#Geometry

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Solution :

General Formula :- For every $n \geq 3$

$n a^2 \ \ [ \frac{1}{4} \cot (\frac{\pi}{n}) - \frac{\pi}{2} + \frac{\pi}{n} ]$

Nikola Alfredi - 1 year, 4 months ago

Answer should be 0 for n = 6.

Shikhar Srivastava - 1 year, 4 months ago

Yes, you are right.. I just took radius $\frac{a}{2}$ ....

Nikola Alfredi - 1 year, 4 months ago

Activated leukocyte cell adhesion (ALCAM) is a member of the immunoglobulin superfamily and is a type of adhesion molecule that was first discovered in malignant melanoma. ALCAM is a transmembrane glycoprotein that is expressed at the junction between epithelial cells and is a member of the immunoglobulin superfamily and is involved in maintaining the stability of tissue structure.

https://www.creative-biogene.com/genesearch/ALCAM.html

Wendy Wilson - 1 year, 10 months ago

I don't understand your comment. Please explain how it is related to my question?

Shikhar Srivastava - 1 year, 10 months ago

I agree with him...

Nikola Alfredi - 1 year, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$