Question

in rhombus abcd below, ae = 11 cm and be = 9 cm. find the area of the rhombus. be sure to include the correct unit in your answer.

Explanation:

Step1: Recall rhombus area formula

The area formula of a rhombus is $A=\frac{1}{2}d_1d_2$, where $d_1$ and $d_2$ are the lengths of the diagonals. In a rhombus, the diagonals bisect each other. So if $AE = 11$ cm and $BE=9$ cm, the diagonals are $d_1 = 2AE$ and $d_2=2BE$.

Step2: Calculate diagonal lengths

$d_1 = 2\times11=22$ cm, $d_2 = 2\times9 = 18$ cm.

Step3: Calculate the area

Using the formula $A=\frac{1}{2}d_1d_2$, we substitute $d_1 = 22$ cm and $d_2=18$ cm. So $A=\frac{1}{2}\times22\times18$. First, $\frac{1}{2}\times22 = 11$, then $11\times18=198$ $cm^{2}$.

Answer:

$198\ cm^{2}$