Question:
A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is ?

Solution:

Interior angle of a regular octagon = (n−2)/n × 180°
= (8−2)/8 × 180° = 135°

Area of square ACEG = a²

In △BAC, using cosine rule:
a² = b² + c² − 2bc·cosC
a² = 6² + 6² − 2(6)(6)cos135°
a² = 72 − (72 × −√2/2)
a² = 72 + 36√2
a² = 36(2 + √2)

Therefore, Area = 36(2 + √2)

Answer: 36(2 + √2)