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Composite Figures

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

Level 3

         

\(ABCD\) 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 \( EFGH \)?

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?

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

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

Square BCDE has side length 12.
Area of triangle ACD is twice the area of square BCDE.
If AD intersects BE at F, what is the area of BCDF?

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?


Source: OBMEP 2016.
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