The measurements of the sides of a triangle are $12 \, cm$,$17 \, cm$,and $25 \, cm$. Find the area of this triangle. (in $, cm^2$)

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 $10 \, cm$.

The ratio of the measures of the sides of a triangle is $3: 4: 6$. If the semiperimeter of the triangle is $39 \, cm$,the measure of the longest side of the triangle is ............ $cm$.

$PQRS$ is a square. If $PR = 10 \, cm$,then the area of $PQRS = \dots \, cm^2$.

Area of a square $= \frac{(\ldots \ldots . .)^{2}}{2} .$

$A$ 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 $m^2$).