Finding area of region? ?

Question

How do i find the area...

A sheep is on a 50 meter chain attached to a corner outside of a triangular fence that is 20 meters each side. Find the area of the grazing region

Answer 1

He will have 5/6 of a 50m circle to graze in without being hampered by the triangular fence.

The area outside the opposite fence to the tethered corner can be broken into three sections. An isosceles triangle of sides 20,30,30 and two arcs of 30m radius.

The angle of the arc is 30 degrees plus half of the apex angle of the triangle.

Sorry but i've run out of time to do the calculations. Hope that helps

p.s. I make the calculation

5/6 of circle is 6544.985

Triangle is 316.228

Area of arc 30m radius 45.74 degrees = 373.378 (twice)

= 7607.97 sq m

Not far off Roko's, probably a rounding error somewhere

Answer 2

grazing area

= 5*π50^2 / 6 + 10*√(30^2-10^2) + 2*(120 - arccos (1/3))*30^2 / 360

= 6250π/3 + 200√2 + 5*(49.471220634490691369246)

= 6544.98469497873591346384 + 282.84271247461900976 + 247.35610317245345684623

= 7075.18351062580838

= 7075.1835 m^2

Answer 3

Area = 7604,9 m2