Explanation:
a) The area of the fish pond is given by the formula:
Area = πr^2
where r is the radius of the pond (which is half of the diameter). So, in this case, r = 10m.
Area = π(10m)^2
Area = 100π m^2
Area ≈ 314 m^2 (rounded to the nearest square meter)
b) The flower border has a width of 2m on the two longer sides and one shorter side of the rectangular park. So, we need to find the area of three strips of land, each of which is 2m wide and has a different length.
The length of the two longer sides is 200m, so the total length of the two strips along these sides is:
2 × 200m = 400m
The length of the shorter side is 100m, but we need to subtract the width of the fish pond (which is 20m) from it, since the flower border does not extend around the pond. So, the length of the strip along this side is:
100m - 20m = 80m
Therefore, the total area of the flower border is:
2m × 400m + 2m × 80m = 960m^2
c) The grassland is the remaining area of the rectangular park after we subtract the area of the fish pond and the flower border from the total area of the park.
The total area of the park is:
200m × 100m = 20,000m^2
The area of the fish pond is:
π(10m)^2 ≈ 314m^2
The area of the flower border is:
960m^2
So, the area of the grassland is:
20,000m^2 - 314m^2 - 960m^2 = 18,726m^2
d) The perimeter of the park is the sum of the lengths of all its sides.
The two longer sides have a length of 200m each, but we need to add the lengths of the two flower borders (each of which is 2m wide), so the total length of the two longer sides is:
200m + 2m + 2m = 204m
The shorter side has a length of 100m, but we need to add the length of the flower border (which is 2m wide), so the total length of the shorter side is:
100m + 2m = 102m
The perimeter of the park is:
204m + 204m + 102m = 510m
Therefore, the perimeter of the park is 510 meters.