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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?

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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

The Pentagon peaches

Five equally sized peaches are closely packed in a pentagon-shaped box. Their midpoints are the vertices of a smaller pentagon. What fraction is shaded?

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?

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Beginner

The tilted brick

A rectangle is covering a square such that they share a diagonal and the top side of the square is divided in half as shown. What fraction of the square is covered by the rectangle? And what fraction of the rectangle is covered by the square?

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?