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# Horse Math Question

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A fence encloses a square field whose sides measure 8 m. A horse is tethered to a rope that is attached to a corner post of the field so that the horse is outside the fence. If the rope holding the horse is 13 m long, find the total grazing area of the horse in square metres.

Feb 27, 2020

#1
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how many are u sending?!

Feb 27, 2020
#2
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A lot lol... just got a new exam review and need someone to explain the solutions to me.

#3
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We  have  two  areas to consider

(1) The horse will be able to  graze a larger  area  which  is the  area  of  a  (3/4)  circle with a radius  of 13

So  this area  =  (3/4) pi *13^2 =   (1/4)pi *  3* 13^2

(2)  We  have two  smaller  areas  that are   both quarter-circles with radii  of (13 - 8)   = 5

So  this area  =    2 (1/4) *pi * 5^2   =  (1/4) pi * 2 * 5^2

So.....the total area =

(1/4) pi  [  3 * 13^2   +  2 * 5^2  ]   =

(pi/4)  [ 507  + 50  ] =

(pi/4)  [ 557]  =

(557/4) pi   m^2  ≈   437.5 m^2    Feb 28, 2020
#4
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thank you so much!