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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The sneak peek
Tag: rectangle
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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?
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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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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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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?
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The Suresh similarity
Two squares and a rectangle. Prove that the red triangles are similar.
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A new slant
Two squares and a slanted rectangle share three vertices. What is the total area?
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Three squares a day
Three congruent squares inscribed in a rectangle. What fraction of the total area is green?
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Slip slidin’ away
Two congruent squares inscribed in a rectangle with given side lengths. What is the total orange area?
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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.