Each side of an equilateral triangle measures $10\,cm$. Find the semi-perimeter of the triangle. (in $,cm$)

$A$ rectangular plot is given for constructing a house, having a measurement of $40 \, m$ long and $15 \, m$ in the front. According to the laws, a minimum of $3 \, m$ wide space should be left in the front and back each, and $2 \, m$ wide space on each of the other sides. Find the largest area where the house can be constructed (in $m^2$).

The sides of a triangle measure $20 \, cm$,$24 \, cm$,and $32 \, cm$. Find its semi-perimeter. (in $, cm$)

In a kite-shaped quadrilateral $ABCD$,$AB = AD = 12 \, cm$,$CB = CD = 17 \, cm$,and $AC = 25 \, cm$. Find its area and the length of diagonal $BD$.

In $\Delta ABC$,$AB = 20 \, cm$,$BC = 48 \, cm$,and $AC = 52 \, cm$,find the area of $\Delta ABC$. (in $, cm^2$)

In quadrilateral $ABCD$, $\angle A = 90^{\circ}$, $AB = 15 \text{ cm}$, $BC = 25 \text{ cm}$, $CD = 12 \text{ cm}$, and $DA = 8 \text{ cm}$. Find the area of quadrilateral $ABCD$. (in $\text{ cm}^2$)