Two regular hexagons inscribed in a square. If the hexagons have side length a and b, what is the square’s side length?
Categories
The honeycomb
Category: Intermediate
Categories
The folded napkin
A square sheet of paper is folded symmetrically from a corner. If the fold length is 4, what is the area of the triangle formed by the other three corners?
Categories
Together we stand
Two squares sharing a vertex. What’s the angle α?
Categories
The pleasure dome
A semicircle with three squares. The areas of the smaller squares are given. What is the area of the biggest one?
Categories
Pyramidion
A triangle containing a semicircle and an equilateral triangle. What fraction is golden?
Categories
Triple dice
An equilateral triangle with three congruent squares. What’s the angle α?
Categories
Paper hat II
Two overlapping congruent right triangles. If |AB|=15 and |BC|=7, what is the total area?
Categories
En garde
An isosceles triangle with two altitudes dividing each other in segments of length 4 and 5. What is the total triangle area?
Categories
Distant peaks
Two isosceles triangles and a right angle. What is the proportion green : gold?
Categories
The Lion King II
A regular hexagon and three squares. What is the proportion yellow : brown?