The problem describes a rhombus-shaped square. The longer diagonal measures 70 meters, and the shorter diagonal is half the length of the longer diagonal. We need to find the area of the square.

1. Problem Description

The problem describes a rhombus-shaped square. The longer diagonal measures 70 meters, and the shorter diagonal is half the length of the longer diagonal. We need to find the area of the square.

2. Solution Steps

Let $D$ be the length of the longer diagonal and $d$ be the length of the shorter diagonal.

We are given that $D = 70$ meters.

The shorter diagonal is half the length of the longer diagonal, so $d = \frac{1}{2} D$.

Substitute $D = 70$ into the equation for $d$:

$d = \frac{1}{2} \cdot 70 = 35$ meters.

The area $A$ of a rhombus is given by the formula:

$A = \frac{1}{2} \cdot D \cdot d$

Substitute the values of $D$ and $d$ into the formula:

$A = \frac{1}{2} \cdot 70 \cdot 35 = \frac{1}{2} \cdot 2450 = 1225$ square meters.

3. Final Answer

The area of the square is 1225 square meters.