Categories
Beginner

The fishing net

Two squares and two equilateral triangles. What fraction is hatched?

Categories
Beginner

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
Advanced

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
Intermediate

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?

Categories
Intermediate

Balancing balls

Two touching circles are placed on top of a right triangle. What’s the angle between the chords connecting the tangency points?

Categories
Beginner

The folded sheet

A rectangular sheet of paper is folded in such a way that two equal angles are formed as shown. What fraction of the resulting quadrilateral is shaded?

Categories
Beginner

Moon over mountains

A rectangular frame encloses two congruent equilateral triangles and a unit circle. What is difference between width and height of the rectangle?

Categories
Intermediate

The triangle tango

An isosceles triangle is attached to another triangle with a 60-degree angle as shown. Their opposite vertices are connected by a line segment of length 2. What is the area of the quadrilateral?

Categories
Intermediate

An Egyptian sunset

A semicircle touches a large equilateral triangle (area equals 9) at its apex and a smaller adjacent equilateral triangle (area equals 1) at its base as shown. What is the total red area?

Categories
Beginner

The tilted hourglass

In a square, a diagonal and a line segment cross at the center. They delimit a tilted hourglass. What fraction of the square is shaded?