Find the area of a triangle whose sides are $13\, cm$,$14\, cm$,and $15\, cm$. (in $, cm^2$)

The base of a right triangle is $8 \, cm$ and its hypotenuse is $10 \, cm$. Its area will be (in $cm^2$):

The sides of a triangle measure $15 \text{ cm}$,$17 \text{ cm}$,and $20 \text{ cm}$. Then,the semi-perimeter of the triangle is ......... $\text{cm}$.

The diagonals of a rhombus are $16\,cm$ and $30\,cm$. Find its perimeter. (in $,cm$)

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 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 $,m^2$)