Answer: 482.8 sq cm
Step-by-step explanation:
The octagon is 8 isosceles triangles. Each has common side r and base 10. The central angle is 360/8 = 45°. By the Law of cosines,
10² = r² + r² - 2 r² cos 45° = 2r²(1 - √2/2) = r²(2-√2)
r² = 100/(2-√2)
The area of a triangle with sides a,b and included angle C is (1/2)ab sin C. Our 8 octagon isosceles triangles each have sides r and r and included angle 45° so our total area, 8 triangles, is
A = 8(1/2) r² sin 45° = (400/(2-√2)) (√2/2) × (2+√2)/(2+√2) = 200(1+√2)
A ≈482.84271
Answer: 482.8 sq cm
