We know that the area of a rhombus can be calculated as:
[tex]A=\frac{1}{2}ab\text{ }[/tex]where a and b are the lengths of the diagonals.
Then the area of the rhombus is:
[tex]A=\frac{1}{2}(40)(30)=600[/tex]Now, we also know that the area can be obtained by:
[tex]A=sh[/tex]where s is the length of the side and h is the height. To obatain the height we need the length of the side. Then lenght of a rhombus is given by:
[tex]s=\sqrt[]{(\frac{a}{2})^2+(\frac{b}{2})^2}[/tex]Then ins this case we have:
[tex]\begin{gathered} s=\sqrt[]{(\frac{40}{2})^2+(\frac{30}{2})^2} \\ s=\sqrt[]{625} \\ s=25 \end{gathered}[/tex]Now that we know the lenght of the side we use the second formula for the area to get h:
[tex]\begin{gathered} 25h=600 \\ h=24 \end{gathered}[/tex]Therefore the height of the rhombus is 24 mm.
