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What is the area of a regular octagon with sides of 2 cm?

Competition practiceGeometry

A8 + 8√ $2 cm^{2}$
B $16 cm^{2}$
C8√ $2 cm^{2}$
D4 + 4√ $2 cm^{2}$

Step-by-Step Solution

A regular octagon of side a is a square of side

a + a 2

with four corner triangles cut off. Area

= 2 (1 + 2) a^{2} = 2 (1 + 2) \times 4 = 8 + 82 cm^{2}

≈

19.3 cm^{2}

.

Answer: A) 8 + 8√

2 cm^{2}

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