Composite Figures

Composite Figures: Level 3 Challenges


The figure below shows a parallelogram with an area of 1. The green points are midpoints of two adjacent sides.

What is the sum of the blue areas?

Which area is larger?

\( ABCD\) is a square inscribed in a circle of diameter \(3\sqrt{2}\). \(E\) and \(F\) are the midpoints of \(AB\) and \(BC\), respectively. What is the area of the shaded region?

From the large right triangle, three smaller right triangles (in white) of respective areas 1, 2, 3 are cut out. Find the area of the remaining figure (in blue), to 2 decimal places.

Construct a square on each side of a triangle with side lengths 3, 4, and 5. Then, construct a hexagon by joining the vertices of the squares which are not vertices of the 3-4-5 triangle.

Find the area of this hexagon.


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