1. The problem is to find the area of a shape with given side lengths 2 m, 5 m, and 4 m. 2. Since the problem does not specify the shape, we assume it is a triangle with sides 2 m, 4 m, and 5 m. 3. To find the area of a triangle when all three sides are known, we use Heron's formula: $$A = \sqrt{s(s-a)(s-b)(s-c)}$$ where $a$, $b$, and $c$ are the side lengths, and $s$ is the semi-perimeter: $$s = \frac{a+b+c}{2}$$ 4. Calculate the semi-perimeter: $$s = \frac{2 + 4 + 5}{2} = \frac{11}{2} = 5.5$$ 5. Substitute values into Heron's formula: $$A = \sqrt{5.5(5.5-2)(5.5-4)(5.5-5)}$$ $$= \sqrt{5.5 \times 3.5 \times 1.5 \times 0.5}$$ 6. Calculate the product inside the square root: $$5.5 \times 3.5 = 19.25$$ $$19.25 \times 1.5 = 28.875$$ $$28.875 \times 0.5 = 14.4375$$ 7. Find the square root: $$A = \sqrt{14.4375} \approx 3.8$$ 8. Therefore, the area of the triangle is approximately 3.8 square meters.