Mid-points of a triangle containing sides $12 \, cm$,$18 \, cm$,and $26 \, cm$ are joined to each other. Find the area of the triangle formed by joining the mid-points.

The area of the shaded region within the square $ABCD$ is . . . . . . $cm^2$. (Assume the side of the square is $28 \ cm$ and it contains four identical circles).

Three metal cubes with edges $6\, cm$,$8\, cm$,and $10\, cm$ respectively are melted together and formed into a single cube. Find the side of the resulting cube (in $cm$).

In $\triangle ABC,$ a line parallel to side $BC$ intersects sides $AB$ and $AC$ at points $D$ and $E$ respectively. Point $D$ divides $AB$ in the ratio $1:4.$ If the area of $\triangle ABC$ is $200 \text{ cm}^2,$ what is the area (in $\text{cm}^2$) of quadrilateral $DECB$?

The lengths of three medians of a triangle are $9 \, cm$,$12 \, cm$,and $15 \, cm$. The area (in $cm^2$) of the triangle is

The difference of the areas of two squares drawn on two line segments of different lengths is $32 \, cm^2$. Find the length of the greater line segment if one is longer than the other by $2 \, cm$. (in $cm$)