Two rectangles are at right angles and have equal area. Prove that the three black lines are parallel.
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Between the lines II
Tag: area
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A golden year
Two squares, a rectangle and a semicircle. What is yellow : green?
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Decorating the tree
A symmetric tree has decorative lines of equal slope, and of lengths 11 and 13. What is the area ratio of green to red to brown?
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The brick pile
Three congruent rectangles inscribed in a triangle. What fraction is brown?
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Compartmentalization
A square with two circles and two common tangents. What’s red : blue?
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Through the roof
A semicircle with its centre. What is green : red in terms of the angles α and β?
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Lemon slice II
A semicircle inscribed in a quarter circle. What fraction is yellow?
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Cuckoo in the nest
Two tangent semicircles inscribed in another semicircle. What is the total area?
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Cozy in his chair
Orange and green semicircles with equally long but perpendicular diameters (both length 2) are partially covered by a blue canopy at angle α. What is the orange area, which is not covered by either of the other regions, in terms of α?
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Stuck in the corner
A square with a diagonal and a right triangle. What fraction is red?