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

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.

How do you find the radius of an inscribed square in a circle?

A circle is inscribed in a square, with a side measuring ‘a’. Find formulas for the circle’s radius, diameter, circumference and area , in terms of ‘a’. As we’ve shown above, the circle’s radius is equal to the half the length of the square’s side, so r=a/2.

What does it mean for a square to be inscribed in another square?

The definition of an “inscribed” square in a square is that all of the smaller square’s vertices lies on the boundaries of the larger square. Notice that for this to happen, the smaller square’s vertices will divide each side of the larger square into two segments, the same on each side.

What will be the area of the circle that can be inscribed in a square of side 10cm write in terms of π?

The area of circle is 25π cm².

What size square can fit in a circle?

The maximum square that fits into a circle is the square whose diagonal is also the circle’s diameter. The length of a square’s diagonal, thanks to Pythagoras, is the side’s length multiplied by the square root of two. Set this equal to the circle’s diameter and you have the mathematical relationship you need.

What happens when a circle is inscribed in a square?

When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle.

How do you find the radius of 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 = π r 2 . Substitute r = 4 in the formula.

What is the area of the inscribe 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 = π r 2 . Substitute r = 4 in the formula. A = π ( 4 ) 2 = 16 π ≈ 50.24. Therefore, the area of the inscribe circle is about 50.24 square units.

How to find the diameter of a circle in a square?

When a circle is inscribed in a square , the diameter of the circle is equal to the side length of the square. You can find the perimeter and area of the square, when at least one measure of the circle or the square is given.