Question

Three equal circles of radius r = 1cm are tangent to each other as shown in the picture. Find the area of the shade region.

Answer 1

You could connect the circle centers to form an equilateral triangle. Then find the area of the triangle. Each corner of the triangle makes a 60 degree angle from the center of the circle, so the "pie" slice inside the circle is 1/6 of the circle area. The area shaded is the equilateral triangle's area minus the 3 pie shaped pieces of the circles.

Answer 2

You mean like this

Answer 3

Right

Answer 4

Then what is the answer?

Answer 5

nw it is a equilateral triangle....ie all angles are 60

Answer 6

So, you need the area of that triangle with side lengths = 2 x radius = 10

Answer 7

Ok you get it here is the answer\[A _{region}=A_{circle}-A_{\triangle}\] \[A _{region}=3{\pi}r^{2}-\frac{ 1 }{ 2 }(2r)^{2}\sin(60^{o})\] \[A _{region}=3{\pi}-\frac{ 1 }{ 2 }\times4\times \frac{ \sqrt{3} }{ 2 }\]Thus the answer is \[A _{region}=(3{\pi}- \sqrt{3})cm^{2} \]

Answer 8

ARea shaded = Area of Triangle - 3 * minor segment

Answer 9

nw u knw the angle.....u have find the are of minor segment