The problem asks to find the area of a rhombus $PQRS$. We are given the length of diagonal $PR = 24$ m and $QT = 7$ m. Since the diagonals of a rhombus bisect each other, we know that $QS = 2 \cdot QT = 2 \cdot 7 = 14$ m. We need to find the area of the rhombus using the lengths of its diagonals.

1. Problem Description

The problem asks to find the area of a rhombus $PQRS$. We are given the length of diagonal $PR = 24$ m and $QT = 7$ m. Since the diagonals of a rhombus bisect each other, we know that $QS = 2 \cdot QT = 2 \cdot 7 = 14$ m. We need to find the area of the rhombus using the lengths of its diagonals.

2. Solution Steps

The area of a rhombus can be found using the formula:

$Area = \frac{1}{2} \cdot d_1 \cdot d_2$, where $d_1$ and $d_2$ are the lengths of the diagonals.

In this case, the diagonals are $PR$ and $QS$. We are given that $PR = 24$ m and we found that $QS = 14$ m.

Substituting these values into the formula, we get:

$Area = \frac{1}{2} \cdot 24 \cdot 14$

$Area = 12 \cdot 14$

$Area = 168$

3. Final Answer

The area of the rhombus is 168 $m^2$.