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

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

An equilateral triangle is sitting on top of a square. What is the radius of the circle that circumscribes this shape?

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.