A square is divided into triangles and quadrilaterals as shown. What fraction of the square area is covered by the shaded triangle?
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The broken window
Tag: area
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The shark fin
An isosceles triangle is inscribed in a semicircle with one side along the diagonal and the top vertex somewhere on the semicircle. What’s the maximum fraction shaded?
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The marble box
Two marbles of sizes π and 4π are enclosed in a rectangular box. What is the total area of the box?
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The folded sheet
A rectangular sheet of paper is folded in such a way that two equal angles are formed as shown. What fraction of the resulting quadrilateral is shaded?
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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?
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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?
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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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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?
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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?