Goat grazing area in an equilateral triangle Q. A goat is tied to the vertex of an equilateral triangle shaped grass field with a rope of 25m . Over what area of the grass field can the goat graze ? Isn't this statement wrong Or can we solve this question with this statement assuming the statement right ?

The angle at the vertex of an equilateral triangle measures $60^\circ$. The goat cannot go outside of the field, presumably, and he cannot go farther than $25 \ \mathrm{m}$ away from the vertex.

Thus the grazable area is the sector of a circle of radius $25 \ \mathrm{m}$ and corresponds to the angle $60^\circ$.

Use the formula $$A=\frac{\theta}{360^\circ}\pi r^2$$ where $\theta$ is in degrees.

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Nevertheless, you are right: the question is not specific enough. For all we know, the triangular field could measure only $1 \ \mathrm{m}$ on each side! That is definitely not a lot of area to graze!

Since the question does not specify the size of the field, we make an inference about what understanding it is testing, and we prove we have that understanding.