Question

Find the perimeter of the figure. https://ka-perseus-graphie.s3.amazonaws.com/eb8635a8059b2c69ad19bf8d44f5a7a7885cf622.png

Answer 1

Answer on Question #54831 - Math - Geometry

Find the perimeter of the figure.

Solution

The figure consists of two squares and two quarters of circle. The perimeter equals $P = AB + \vec{BM} + MN + NK + \vec{KD} + DA$ .

It is given that $AB = MN = NK = AD = 4$

Arcs $\vec{BM},\vec{KD}$ are equal, because they have the same radius $R = 4$ ( $R = MC = CK$ ) and subtend equal angles $90{}^{\circ}$ .

So $\vec{BM} = \vec{KD} = \frac{1}{4} * 2\pi R = \frac{\pi R}{2} = 2\pi$ .

Finally $P = 4 + 2\pi + 4 + 4 + 2\pi + 4 = 16 + 4\pi$

Answer: $P = 16 + 4\pi$

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