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Advanced

The sneak peek

A rectangle with given side lengths is folded back and forth such that the corner touches the opposite side as shown. What is the minimal shaded fraction?

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Intermediate

House of Orange

A right triangle with a red and yellow square attached. Two circular arcs centered in the triangle vertices. What is the area of the orange rectangle in terms of red and yellow?

Categories
Intermediate

Take five origami

Divide a rectangular piece of paper in five pieces of equal area. You only have a pair of scissors at your disposal, but you are allowed to make straight folds to guide you.

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Beginner

The voting pencil

A square and a rectangle share a vertex. Two triangle areas are given. What is the total area?

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Intermediate

The yardstick

A rectangle containing a circle and a line segment connecting the top side to the bottom tangency point. What is its area in terms of lengths a and b?

Categories
Intermediate

The Suresh similarity

Two squares and a rectangle. Prove that the red triangles are similar.

Categories
Intermediate

A new slant

Two squares and a slanted rectangle share three vertices. What is the total area?

Categories
Beginner

Three squares a day

Three congruent squares inscribed in a rectangle. What fraction of the total area is green?

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Intermediate

Slip slidin’ away

Two congruent squares inscribed in a rectangle with given side lengths. What is the total orange area?

Categories
Intermediate

Overlapping interests

A square, a rectangle and a circle that partially overlap. One square vertex coincides with a rectangle-circle tangency point. Prove that the area of the square equals that of the rectangle.