Question

find the area of the rhombus

Explanation:

Step1: Recall the formula for the area of a rhombus

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

Step2: Determine the lengths of the diagonals

From the diagram, one diagonal \( d_1 \) is the sum of the two 13 cm segments, so \( d_1=13 + 13=26 \) cm. The other diagonal \( d_2 \) is the sum of the two 4 cm segments, so \( d_2 = 4+4 = 8 \) cm.

Step3: Calculate the area

Substitute \( d_1 = 26 \) cm and \( d_2=8 \) cm into the formula:
\( A=\frac{1}{2}\times26\times8 \)
First, calculate \( 26\times8 = 208 \), then \( \frac{1}{2}\times208=104 \).

Answer:

104