Geometry

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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