# how to calculate the area of ​​a rhombus is in $cm^2$

How do I calculate the area of ​​a rhombus is in $cm^2$?

Is the formula $\frac12 \times 17 \times 16$? Anyone can help me to solved this? I don't know the rhombus formula.

Based on my exercise book, the answer is $240 cm^2$

– user67258
Jul 26, 2013 at 3:13

Hint: You can draw the vertical diagonal of the rhombus, which will cut the 16 cm diagonal in half and make the rhombus into four right triangles.

You did some of the work by now.

You just have to be more careful.

If you noticed by cutting the $17$cm by $16$cm by $17$cm isoceles triangle in half you can figure out its height by using the pythagorean theorem. $a^2 + b^2 = c^2$.

This means that the height of the triangle, let's say $b$, is $(8\text{cm})^2 + b^2 = (17\text{cm})^2$

or $b = 15\text{cm}$.

Recall that the area of a triangle is $.5 \times b \times h$. So this means that the area of the large $17$ by $16$ by $17$ triangle is $.5 \times 16\text{cm} \times 15\text{cm}$ since the height of the triangle is $15$. Since two of these triangles make up the area of the rhombus however, we have $2 \times .5 \times 16\text{cm} \times 15\text{cm or }16\text{cm} \times 15\text{cm} = 240\text{cm}^2$.

One more thing I would like to add: because a rhombus is a particular type of parallelogram, the area of formula for a rhombus is the same as the area formula of a parallelogram: $A = base \times height = b \times h$. In this case however, finding the height of the rhombus required more trigonometry than was needed to solve the problem. So the best method was decomposing the rhombus into two triangles.

Your edited attempt is close, but not quite. After drawing the vertical diagonal, you have a right triangle with hypotenuse $17\,\text{cm}$ and base $8\,\text{cm}$.

To find the height, we must use the Pythagorean Theorem: $$b^2 + h^2 = c^2$$ Where $b$ is the base of the triangle, $h$ is the height, and $c$ is the hypotenuse.

See if you can find the height of the triangle... Let me know in a comment if you need more help.