How do you find the area of a square with an inscribed circle?

When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. That is, the diameter of the inscribed circle is 8 units and therefore the radius is 4 units. The area of a circle of radius r units is A=πr2 .

What is the ratio of the area of a square inscribed in a circle?

π:2
Now, ratio of area of the circle and the square =πr2a2=πr22r2=π:2.

How do you find the area of an inscribed square?

The radius is half the diameter, so r=a·√2/2 or r=a/√2. The circumference is 2·r·π, so it is a·√2·π. And the area is π·r2, so it is π·a2/2.

What is the meaning of inscribed square?

Definition. A square is a four-sided figure in which all four sides are equal in length and all four angles are 90 degree angles. An inscribed square is a square drawn inside a circle in such a way that all four corners of the square touch the circle.

When a square is inscribed in a circle what are its properties?

When a square is inscribed in a circle, we can derive formulas for all its properties- length of sides, perimeter, area and length of diagonals, using just the circle’s radius. Conversely, we can find the circle’s radius, diameter, circumference and area using just the square’s side. A square is inscribed in a circle with radius ‘r’.

How to find the area of a circle with radius?

The area of a circle is pi times the square of its radius. The radius is half the diameter. Area = π * (Diameter / 2)2 Diameter of a Circle

What is the sum of the area of a shaded circle?

The sum of their areas is the difference between the area of the circle and the area of the square. If we have the side of the square, a, we get A shaded = (A circle -A square )/4= (π·a 2 /2 -a 2 )/4= (π-2)·a 2 /8.

Why is the radius of a circle equal to half the square?

Here, a similar key insight is that the circle’s radius is equal to half the square’s side length. Since the circle is inscribed in the square, the square’s side is tangent to the circle. By definition, the radius is perpendicular to the tangent line at the point of tangency. The radius forms a 90° angle with one side of the square.