Question

find the area of the rhombus.
image of a rhombus with diagonals: one diagonal is split into two 15 m segments, the other diagonal is split into two 8 m segments
? m²

Explanation:

Step1: Recall the formula for the area of a rhombus

The area of a rhombus is given by the formula \( A=\frac{1}{2}d_1d_2 \), where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.

Step2: Identify the lengths of the diagonals

From the diagram, one diagonal \( d_1 = 15 + 15=30\) m (since the two segments of the diagonal are each 15 m) and the other diagonal \( d_2=8 + 8 = 16\) m (since the two segments of the other diagonal are each 8 m).

Step3: Calculate the area

Substitute \( d_1 = 30 \) m and \( d_2=16 \) m into the formula:
\( A=\frac{1}{2}\times30\times16 \)
First, calculate \( 30\times16 = 480 \), then \( \frac{1}{2}\times480=240 \).

Answer:

240