The problem asks for the area of the rhombus HEFG. We are given that $HF = 13$ cm and $EG = 10$ cm.

1. Problem Description

The problem asks for the area of the rhombus HEFG. We are given that $HF = 13$ cm and $EG = 10$ cm.

2. Solution Steps

The area of a rhombus can be calculated using the lengths of its diagonals. Let $d_1$ and $d_2$ be the lengths of the two diagonals of a rhombus. The formula for the area of the rhombus is:

$Area = \frac{1}{2} \times d_1 \times d_2$.

In our case, the lengths of the diagonals are $HF = 13$ cm and $EG = 10$ cm.

Therefore, $d_1 = 13$ cm and $d_2 = 10$ cm.

Now, we can plug these values into the formula:

$Area = \frac{1}{2} \times 13 \times 10 = \frac{1}{2} \times 130 = 65$.

Since the lengths are given in cm, the area will be in square centimeters (cm$^2$).

3. Final Answer

65 cm$^2$