Final answer:
To calculate the area of a circular garden with a circumference of 20 meters, first find the radius using the formula for circumference, and then use the area formula. The radius is approximately 3.2 meters, and the area is approximately 32 square meters after rounding to the nearest whole number.
Step-by-step explanation:
The question asks us to calculate the area of a circular garden whose perimeter, also known as the circumference, is 20 meters. To find the area, we need to determine the radius. The formula for the circumference of a circle is C = 2πr. With a circumference of 20 meters and using 3.14 for π, we can solve for the radius (r) as follows:
C = 2πr → 20 m = 2 × 3.14 × r → r = 20 m / (2 × 3.14) → r = 3.1847 m
However, since the question requires us to use only two significant figures for π, the radius should also be rounded to two significant figures, which gives us r ≈ 3.2 m. Now that we have the radius, we can calculate the area, A, using the formula A = πr²:
A = πr² = 3.14 × (3.2 m)² = 3.14 × 10.24 m² ≈ 32.1536 m²
Rounding to the nearest whole number, the area of the garden is approximately 32 m². It's important to note that the area of the circle will be less than the area of a square with a side of 2r (covering the diameter).