Area of a rhombus $=$ ............

In quadrilateral $ABCD$,$AB = 9 \, cm$,$BC = 13 \, cm$,$CD = 14 \, cm$,$DA = 12 \, cm$,and $BD = 15 \, cm$. Find the area of quadrilateral $ABCD$ 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 $12 \, cm.$

The sides of a triangular plot are in the ratio of $4: 7: 9$ and its perimeter is $500 \, m$. Find its area.

Write True or False and justify your answer.
The area of an equilateral triangle is $20 \sqrt{3} \text{ cm}^2$ whose each side is $8 \text{ cm}$.

An isosceles right triangle has an area of $8 \, cm^{2}$. The length of its hypotenuse is