A diagonal of a rhombus divides it into two congruent triangles of equal area.

Area of a quadrilateral whose sides and one diagonal are given can be calculated by dividing the quadrilateral (along the given diagonal) into two triangles and using Heron's formula.

If the area of the shaded region in the figure given below is $k {\mathrm{cm}}^2$, find $k$.

How much paper of each shade is needed to make a kite given in the adjoining figure, in which $ABCD$ is a square with diagonal $44 \mathrm{cm}$ ?

A design is made on a rectangular tile of dimensions $70 \mathrm{cm}\times 50 \mathrm{cm}$ as shown in the figure below. The design shows $8$ triangles, each of sides $26 \mathrm{cm}, 17 \mathrm{cm}$ and $25 \mathrm{cm}$. Find the total area of the design and the remaining area of the tile.