The area of a heptagon inscribed in a circle with a radius of 1 inch is approximately 3.63 square inches.
A 7-sided figure is also known as a heptagon.
We can use the area formula of a regular polygon inscribed in a circle to find the area of the heptagon with a radius of 1:
Area of a regular polygon = n * r^2 * sin(2π/n) / 2
Where:
The number of sides = n
The radius of the circle = r.
Plugging in the given values:
The area of a heptagon = 7 * 1^2 * sin(2π/7) / 2
The area of a heptagon ≈ 3.6339 = 3.63 in²
Thus, we can conclude that the area of a 7-sided figure or heptagon inscribed in a circle with a radius of 1 inch is approximately 3.63 square inches.