The area of an equilateral triangle is equal to ............

In quadrilateral $ABCD$,$AB = 40 \, cm$,$BC = 35 \, cm$,$CD = 48 \, cm$,$DA = 29 \, cm$ and $BD = 29 \, cm$. Find the area of quadrilateral $ABCD$. (in $, cm^2$)

The shape of a field is a triangle. The measurements of the sides of the field are $51 \,m$,$52 \,m$ and $53 \,m$. Find its area. (in $,m^2$)

Calculate the area of the shaded region in the figure.

The sides of $\Delta PQR$ measure $13 \, cm$, $14 \, cm$, and $15 \, cm$. Find its area in $cm^2$.

State whether each of the following statements is true or false:
$(1)$ If the side of an equilateral triangle is $10 \, cm,$ then its semi-perimeter is $30 \, cm.$
$(2)$ In an isosceles triangle,the length of two equal sides is $20 \, cm,$ then its semi-perimeter is $20 \, cm.$
$(3)$ In $\Delta ABC,$ $\angle B = 90^{\circ},$ $AB = 6 \, cm$ and $BC = 8 \, cm,$ then its semi-perimeter is $12 \, cm.$