Problems

In a square $ABHI$ two smaller squares are drawn: $ACFG$ with area equal to $16$ and $BCED$ with area equal to $4$. Find the area of hexagon $DEFGIH$.

If each of the small squares has an area of $1$, what is the area of the triangle?

Divide the parallelogram into two parts such that they can be reassembled to make a triangle.

Cut a triangle into three parts, which can be reassembled into a rectangle.

On the diagram each number denotes the area of a rectangle it is written into. What are the areas of the other rectangles?

Draw any quadrilateral with all sides of different length and divide it into $5$ polygons of equal area.

Line $AB$ is parallel to line $CD$ and line $AD$ is parallel to line $BE$. Show that triangles $ADE$ and $ABC$ have equal areas.

A quadrilateral $ABCD$ is given. Points K and L belong to the side $AB$ and $AK=KL=LB$ and points $N$ and $M$ belong to the side $CD$ and $CM=MN=ND$. Show that the area of the quadrilateral $KLMN$ is $\frac{1}{3}$ of the area of the quadrilateral $ABCD$.

A quadrilateral $ABCD$ is given. Point $M$ is a midpoint of $AB$ and point $N$ is a midpoint of $CD$. Point $P$ is where segments $AN$ and $DM$ meet, point $Q$ is where segments $MC$ and $NB$ meet. Show that the sum of areas of triangles $APD$ and $BCQ$ is equal to the area of the quadrilateral $MQNP$.

The marked angles are all ${45}^{\circ }$. Show that the total green and blue areas are the same.