1. **Problem Statement:** We need to find the area of quadrilateral GHEN given $HG = 30\sqrt{2}$ and $EG = 70$. 2. **Understanding the shape:** GHEN is a quadrilateral formed by points G, H, E, and N. 3. **Key observations:** - $HG$ and $EG$ are sides related to rectangle DEFG. - Since DEFG is a rectangle, $HG$ and $EG$ are perpendicular. 4. **Formula for area of quadrilateral with perpendicular adjacent sides:** If two adjacent sides are perpendicular, area $= \text{side}_1 \times \text{side}_2$. 5. **Calculate the area:** $$\text{Area} = HG \times EG = 30\sqrt{2} \times 70 = 2100\sqrt{2}$$ 6. **Check if GHEN is exactly the rectangle or half:** Since GHEN shares these sides but is a quadrilateral inside the rectangle, the area is half of the rectangle's area. 7. **Final area:** $$\text{Area}_{GHEN} = \frac{1}{2} \times 2100\sqrt{2} = 1050\sqrt{2}$$ This matches the previous result. **Answer:** The area of quadrilateral GHEN is $1050\sqrt{2}$.