Olimpiad Math Question

[dark shadow]

A goat is tied with a 10-meter rope to a corner of a rectangular barn measuring 8m × 5m. The barn is surrounded by grass. What is the area (in m²) that the goat can graze?
Answer choices:

259.87 m²

258.265 m²

268.625 m²

286.725 m²

[karmic pike]

That's a nice one, what have you tried?

[dark shadow]

I still can't visualize this problem.

[sonic harness]

If it were me I would start by drawing a picture of the barn and draw a circle around one corner of the barn

The circle would have a radius of 10m, the length of the rope. You can kinda picture the goat running around the corner of the barn with the rope.

[hazy rover]

does it mean the area filled with grass in reach of the goat?

[dawn hornet]

it's more like 1/4 of a circle

so like

the goat can move 10m or 5m

[dawn hornet]

i think the diagram is supposed to look like this (radius 5)

and since BC = 5

then you got a semi circle

[dawn hornet]

oh cool then the circle would cover the entire barn

[karmic pike]

Radius is 10 from what I understand

[dawn hornet]

but if the radius is 10 then the circle would just cover the whole barn 😭

[karmic pike]

Ah good point

[karmic pike]

But that's what we want no?

The question is how much can the cow go outside of the barn

[dawn hornet]

oh alright

then easy

area of circle - 40

[karmic pike]

Makes things easier yeah

[dawn hornet]

💀

[karmic pike]

Haha yeah we don't have the same Olympiad questions I guess 😅

[karmic pike]

Do you find one of the options?

[dawn hornet]

no

it says 274. something

[karmic pike]

Then I don't understand the question

[dark shadow]

yeah, i get the answer broh

from my teacher

258,265

[lyric swallow]

Idt its that easy bcz it's tied by a rope ryt

And one of the ends of rope is tied to one corner of the barn

When it encounters another corner the radius would shrink to 10-5 or 10-8 uk

So I think it will be like area of semicircle with radius 10 + area of quater circle with radius 2 + area of quater circle with radius 5

[hazy rover]

in this case I think it's just area of circle - area of barn

cuz 8² + 5² < 10²

and 8 < 10 and 5 < 10

thus going around will not cut any corners

but the result is 274.159... which is not one of the options

[opaque parcel]

My interpretation of the question is such that the goat is allowed to graze outside the barn WITH the rope being becoming pivoted at other corners of the barn