A regular octagon is coloured as shown. What fraction of its area is red?

# Month: November 2020

## The party hat

A cone has height 6 and base diameter 6. On it lie two points, one exactly halfway up, the other diametrically opposed at the base. What’s the shortest distance between these points going along the cone surface?

## The windshield wipers

A square and two rectangles, connected by two circular arcs, form a square. What is the proportion of the orange to the green area?

## Velocipede II

Two circles of area π and 9π respectively are contained in a parallelogram. What’s its area?

## The pyramid perspective

Two congruent pyramids placed at different distances from the observer appear as equilateral triangles in a square frame. If the closest one is at 100 meter, how far is the distant pyramid?

## The square peg

A square is fitted into an equilateral triangle as shown. What fraction is shaded?

## The Pacman principle

In a circle, two congruent chords are connected in a point. A line segment is drawn through the circle center as shown, forming two angles. What is the proportion α : β?

## The velocipede

Two circles are embedded in a frame of size 9 x 8. What is their total area?

## The blue diamond

Two isosceles triangles are placed as shown. What is the proportion of the line segments a and b?

## The askew envelope

In a square, an interior point is drawn with an angle to the top vertices of 120°. What’s the angle between the chords formed by the two arcs centered in these vertices?