The lengths of the sides of a triangle are $13 \, cm$,$13 \, cm$,and $10 \, cm$. Find its area. Also,find the length of the altitude from the opposite vertex to the side whose length is $10 \, cm$.

$A$ plot,in the shape of a quadrilateral $XYZW$,has $XY = 25 \, m$,$YZ = 60 \, m$,$ZW = 33 \, m$,$WX = 34 \, m$,and $XZ = 65 \, m$. Find its area. (in $, m^2$)

The sides of a triangle are $a \, cm$,$b \, cm$,and $c \, cm$. Also,its semi-perimeter is $s \, cm$. If $s - a = 10 \, cm$,$s - b = 15 \, cm$,and $s - c = 12 \, cm$,then $s = \dots \, cm$.

$A$ rhombus shaped field has green grass for $18$ cows to graze. If each side of the rhombus is $30\, m$ and its longer diagonal is $48\, m$,how much area of grass field will each cow be getting (in $, m^{2}$)?

Find the area of the triangle with the side lengths $51 \, cm$,$52 \, cm$,and $101 \, cm$. (in $, cm^2$)

Sanya has a piece of land which is in the shape of a rhombus (see figure). She wants her one daughter and one son to work on the land and produce different crops. She divided the land into two equal parts. If the perimeter of the land is $400\, m$ and one of the diagonals is $160\, m$,how much area will each of them get for their crops (in $, m^2$)?