A geometry problem by Interliser 727

Geometry Level 4

As of above, a goat is tied on a corner of a pentagon with a rope 7 in length, and all around are grass. The side length of the pentagon is 3 in length.

What is the area of grass the goat can eat? (Use $\pi$ $=3$ )

The answer is 123.3.

1 solution

Steven Chase
Jul 15, 2018

The grazing area consists of several partial circles. The area of a partial circle is:

$\large{A = \frac{1}{2} r^2 \, \theta}$

The quantity $r$ is the radius of the partial circle, and $\theta$ is the angle measure ( $\theta = 2 \pi$ would correspond to a full circle). Adding the area contributions from all partial circles, and using the approximation $\pi = 3$ , yields a total grazing area of $123.3$ .

A geometry problem by Interliser 727

The answer is 123.3.

1 solution

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