First, consider that the sum total of the four interior angles in any rhombus must equal \(\displaystyle 360$^\circ$\). Secondly, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of \(\displaystyle 180$^\circ$\). 

One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with \(\displaystyle 46$^\circ$\). Therefore, find the difference between \(\displaystyle 180$^\circ$\) and \(\displaystyle 46$^\circ$\) to find the solution. 

\(\displaystyle 180-46=134$^\circ$\)

A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of \(\displaystyle 180$^\circ$\). 

One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with \(\displaystyle 159$^\circ$\). Find the difference between \(\displaystyle 180$^\circ$\) and \(\displaystyle 159$^\circ$\) to find the solution. 

\(\displaystyle 180-159=21$^\circ$\)

To solve this problem, consider that the sum total of the four interior angles in any rhombus must equal \(\displaystyle 360$^\circ$\). Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of \(\displaystyle 180$^\circ$\).

Since this problem provides the measurement for two of the interior angles, find the sum of those two angles. Then subtract that sum from \(\displaystyle 360$^\circ$\) to find the sum of the two remaining interior angles.

The solution is:

\(\displaystyle 121+121=242\)

\(\displaystyle 360-242=118$^\circ$\)

Note: this means that each of the two remaining angles must have a measurement of \(\displaystyle 59$^\circ$\).  

Write the formula for the area of a rhombus.

\(\displaystyle A=\frac{d_1\cdot d_2}{2}\)

Plug in the given area and diagonal length. Solve for the other diagonal.

\(\displaystyle 60\:cm^2=\frac{2\:cm\cdot d_2}{2}\)

\(\displaystyle 2(60\:cm^2)=2(\frac{2\:cm\cdot d_2}{2})\)

\(\displaystyle 120\:cm^2=2\:cm\cdot d_2\)

\(\displaystyle \frac{120\:cm}{2\:cm}=\frac{2\:cm\cdot d_2}{2\:cm}\)

\(\displaystyle d_2 =60\:cm\)

The equation for the area of a rhombus is given by:

\(\displaystyle A= \frac{p \cdot q}{2}\)

where \(\displaystyle p\) and \(\displaystyle q\) are the two diagonal lengths. 

This problem very quickly becomes one of the "plug and chug" type, where the given values just need to be substituted into the equation and the equation then solved. By plugging in the values given, we get:

\(\displaystyle A = \frac{12\:cm \cdot 6\:cm}{2}\)

\(\displaystyle A = \frac{72\:cm^2}2{}\)

\(\displaystyle A= 36\:cm^2\)

Write the formula for the area of a rhombus:

\(\displaystyle A=\frac{d_1 \cdot d_2}{2}\)

Substitute the given lengths of the diagonals and solve:

\(\displaystyle A=\frac{d1 \cdot d2}{2} = \frac{20\:cm \cdot 40\:cm}{2} =\frac{800\:cm^2}{2} = 400\:cm^2\)

Write the formula for finding the area of a rhombus. Substitute the diagonals and evaluate.

\(\displaystyle A=\frac{d1\cdot d2}{2}= \frac{2a \cdot 5a^2}{2}= 5a^3\)

Write the formula to find the perimeter of a rhombus.

\(\displaystyle P=4s\)

Substitute the side length and simplify.

\(\displaystyle P=4(\frac{1}{2})=2\)

Write the formula to find the perimeter of a rhombus.

\(\displaystyle P=4s\)

Substitute the side length and solve.

\(\displaystyle P=4(9)=36\)

Write the formula for the perimeter of a rhombus.

\(\displaystyle P=4s\)

Substitute the side length and solve for the perimeter.

\(\displaystyle P=4\left(\frac{11}{8}a+\frac{1}{2}b\right) = \frac{11}{2}a+2b\)