8. \( A=\frac{1}{2} b h \), when \( A=200 \mathrm{ft} \) and \( h=10 \mathrm{ft} \)

To find the base \( b \) of the triangle using the formula \( A=\frac{1}{2} b h \), we can rearrange the equation. Since \( A = 200 \) ft² and \( h = 10 \) ft, we substitute these values into the equation to get \( 200 = \frac{1}{2} b (10) \). This simplifies to \( 200 = 5b \). Dividing both sides by 5 gives \( b = 40 \) ft. So, the base of the triangle is 40 ft! This equation for the area of a triangle isn’t just useful in math class; it shows up everywhere from architecture to landscaping. For example, architects use this equation to determine the area of triangular roofs or garden plots, ensuring that their designs maximize space while maintaining aesthetic appeal. So, next time you see a triangular shape, you can impress your friends with your area knowledge!