Find the area of a regular octagon inscribed in a circle of radius 10 cm
Answers
= 8 * (1/2) * (10)^2 sin45 degrees
= 200√2 sq. cms.
Given:
A regular octagon is inscribed in a circle of radius 10cm.
To Find:
The radius of the regular octagon.
Solution:
The given problem can be solved using Simple geometry.
1. The radius of the circle is 10cm.
2. The octagon can be divided into 8 similar triangles as shown in the figure below.
3. Hence the area of the octagon will be equal to 8 times the area of the triangle.
4. Since the center of the octagon is divided into 8 parts, every triangle occupies an area of (360/8) = 45°.
5. The length of the two adjacent sides containing the angle 45° is 10cm, 10cm.
6. The area of a triangle having an angle α and having the two adjacent sides a and b which contains the angle α is given by the formula,
=> A = (1/2) x a x b x Sin(α).
=> Area of the triangle = 1/2 x 10 x 10 x sin(45°),
=> Area of the triangle = 100/2√2,
=> Area of the triangle = 25√2 cm².
7. Area of the octagon = 8 x area of the triangle,
=> Area of the octagon = 8 x 25√2 ,
=> Area of the octagon = 200√2cm².
Therefore, the area of the octagon inscribed in a circle of radius 10 cm is 200√2 cm².
