The diameter of a circle is 4 m . Find its area in terms of \( \pi \).

To find the area of a circle, you can use the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle. Since the diameter is 4 m, the radius is half of that, which gives us \( r = 2 \) m. Plugging that into the formula, we get: \[ A = \pi (2)^2 = \pi (4) = 4\pi \] So, the area of the circle is \( 4\pi \) square meters. Did you know that circles have been studied by mathematicians since ancient times? The ancient Greeks were particularly fascinated with their properties, and they even discovered the relationship between a circle's diameter and its circumference, known today as \( \pi \). This number, approximately 3.14, pops up all over the place—not just in geometry, but in physics and engineering too! In practical terms, knowing how to calculate the area of a circle is super handy! Whether you're designing a garden layout, determining the amount of grass seed needed for a round patch, or even figuring out the size of a decorative tablecloth for a circular table, this formula comes to the rescue. It's a small calculation that can have a big impact on your projects!