Subjects geometry

Development Area

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Development Area


1. **State the problem:** We want to find the area of a right triangle with legs each measuring $\frac{1}{2}$ mile and compare it to the total area of 50 football pitches. 2. **Convert units:** One mile equals 1600 meters. Therefore, $\frac{1}{2}$ mile = $\frac{1}{2} \times 1600 = 800$ meters. 3. **Calculate the area of the triangle:** The area of a right-angled triangle is given by: $$\text{Area} = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2$$ Substituting: $$\text{Area} = \frac{1}{2} \times 800 \times 800 = \frac{1}{2} \times 640000 = 320000 \text{ m}^2$$ 4. **Calculate the area of one football pitch:** Each pitch measures 100 m by 50 m. Area = $100 \times 50 = 5000$ m$^2$ 5. **Calculate the total area of 50 football pitches:** $$50 \times 5000 = 250000 \text{ m}^2$$ 6. **Compare the areas:** Area of development = 320000 m$^2$ Area of 50 pitches = 250000 m$^2$ Since $320000 > 250000$, the development area is greater. **Final answer:** The area of the development ($320000$ m$^2$) is greater than the total area of 50 football pitches ($250000$ m$^2$).