An equilateral triangle is folded with its left side at right angles with the base. What fraction of the total triangle is shaded?
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The folded triangle
Author: Rik D. Tangerman
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The green kimono
An equilateral triangle and three squares. What’s the angle?
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The wheelbarrow
A circle and two semicircles are nested as shown. What’s the proportion of their respective radii a : b : c ?
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The circus tent
A regular octagon is coloured as shown. What fraction of its area is red?
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The party hat
A cone has height 6 and base diameter 6. On it lie two points, one exactly halfway up, the other diametrically opposed at the base. What’s the shortest distance between these points going along the cone surface?
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The windshield wipers
A square and two rectangles, connected by two circular arcs, form a square. What is the proportion of the orange to the green area?
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Velocipede II
Two circles of area π and 9π respectively are contained in a parallelogram. What’s its area?
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The pyramid perspective
Two congruent pyramids placed at different distances from the observer appear as equilateral triangles in a square frame. If the closest one is at 100 meter, how far is the distant pyramid?
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The square peg
A square is fitted into an equilateral triangle as shown. What fraction is shaded?
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The Pacman principle
In a circle, two congruent chords are connected in a point. A line segment is drawn through the circle center as shown, forming two angles. What is the proportion α : β?