sarzan wrote:

alpha_plus_gamma wrote:

B

Heres how

perimeter of the circular part

3/4* circumference

3/4 * 2 *pi * 2 = 3 * pi

calculate the base of the isosceles triangle, connect the base of the triangle to centre of circle to form triangle.

the arc = 1/4th of circumference

so the central angle is 90 => right angle triangle

two sides of the triangle = radius of circle = 2 each

so base of isosceles triangle sqrt(8)

height of external isoceles triangle= 5

length of the side of external traingle a: a2 = 5^2 + [sqrt(8)/2]^2 = 25 + 2 = 27 i.e length of side = 3* sqrt(3)

perimeter = 3* pi + 2* 3 * sqrt(3)

How did you get the base of isosceles triangle sqrt(8) ?

Attachment:

geometry.JPG [ 11.12 KiB | Viewed 916 times ]
I am bad at drawing, but the attached image may help you.

Arc AB = 1/4 ( since remaining part is 3/4 of circumference)

therefore the central angle is 1/4 of 360 = 90 degrees. making OAB right angle triangle.

sides of the triangle are radii of circle = 2

and the hypotenuse = \(sqrt (2^2 + 2^2)\)