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?
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?
Which has the greatest area, a circle or a square inscribed in an
isosceles, right angle triangle?
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
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9,
12, 15... other squares? 8, 11, 14... other squares?
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
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 sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.
An equilateral triangle is sitting on top of a square.
What is the radius of the circle that circumscribes this shape?