A regular octagon is coloured as shown. What fraction of its area is red?
Categories
The circus tent
Tag: triangle
Categories
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?
Categories
The square peg
A square is fitted into an equilateral triangle as shown. What fraction is shaded?
Categories
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?
Categories
The blue diamond
Two isosceles triangles are placed as shown. What is the proportion of the line segments a and b?
Categories
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?
Categories
The fishing net
Two squares and two equilateral triangles. What fraction is hatched?
Categories
The broken window
A square is divided into triangles and quadrilaterals as shown. What fraction of the square area is covered by the shaded triangle?
Categories
The shark fin
An isosceles triangle is inscribed in a semicircle with one side along the diagonal and the top vertex somewhere on the semicircle. What’s the maximum fraction shaded?
Categories
The corner pocket
A snooker player wants to corner a ball starting from a point on one side and bouncing two times from the opposite sides. Given the dimensions of the table in the figure, what’s the length of the track the snooker ball travels?