Problems

Age
Difficulty
Found: 1974

The area of the triangle AEC is 4, the area of the triangle BCE is 9, the area of the triangle ABC is 21. What is the area of the triangle ADE?

A series of squares are connected by touching vertices. Some triangles were drawn outside and inside of the chain. Show that the total green area is the same as the total red area.

In a triangle ABC, D is the midpoint of BC, and E is the midpoint of AD. F is the intersection of the side AC with BE. What is the area of the triangle AEF as a proportion of the area of the triangle ABC?

Let ABCD be a parallelogram. The segment EF is parallel to the diagonal BD, and the segment EG is parallel to the diagonal AC. Show that the areas of the triangles EFD and EGC are equal.

In a trapezium ABCD, the side AB is parallel to the side CD. Prove that the areas of triangles ABC and ABD are equal.

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The triangle visible in the picture is equilateral. The hexagon inside is a regular hexagon. If the area of the whole big triangle is 18, find the area of the small blue triangle.

On the left there is a circle inscribed in a square with side 1. On the right there are 16 smaller, identical circles, which all together fit inside a square of side 1. Which area is greater, the yellow or the blue one?

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In a parallelogram ABCD, point E belongs to the side CD and point F belongs to the side BC. Show that the total red area is the same as the total blue area:

The figure below is a regular pentagram. What is larger, the black area or the blue area?

A circle is inscribed in a square, and another square is inscribed in the circle. Which area is larger, the blue or the orange one?