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Overlap, inscribe, and circumscribe a collection of simple geometric shapes to make a complex, composite figure. See more

\(ABCD\) is a square of side length 1. Points \(E, F, G, H \) are such that \( AE : EB = 1:1\), \( BF: FC = 1 : 2 \), \( CG : GD = 1 : 3 \), \( DH : HA = 1 : 4 \).

What is the area of the quadrilateral \( EFGH \)?

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In a square, we draw a semicircle on the left side.

We also draw an isosceles triangle on the right side, with its apex at the center of the semicircle.

Which has a larger area, the yellow sector or the blue sector?

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The side of the square is \( a \). Express the green area with \( a \).

Each square's vertex is a circumcentre of appropriate circular arc.

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Area of triangle ACD is twice the area of square BCDE.

If AD intersects BE at F, what is the area of BCDF?

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Two right triangles, both with legs measuring \(a\) and \(b\), where \(a>b\), are overlapping as the image above.

What is the area of the gray quadrilateral?

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