Question

given km = 15.3 and ln = 30.3, find the area of rhombus klmn. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Recall the formula for the area of a rhombus

The area of a rhombus can be calculated using the formula \(A = \frac{1}{2}d_1d_2\), where \(d_1\) and \(d_2\) are the lengths of the diagonals. In rhombus \(KLMN\), let \(d_1 = LN = 30.3\) and \(d_2=KM = 15.3\).

Step2: Substitute the values into the formula

Substitute \(d_1 = 30.3\) and \(d_2 = 15.3\) into the formula \(A=\frac{1}{2}d_1d_2\). So, \(A=\frac{1}{2}\times30.3\times15.3\).
First, calculate \(30.3\times15.3=(30 + 0.3)\times(15+0.3)=30\times15+30\times0.3+0.3\times15 + 0.3\times0.3=450+9 + 4.5+0.09 = 463.59\).
Then, \(A=\frac{1}{2}\times463.59 = 231.795\).

Answer:

\(231.8\)