Maria building a vegetable garden the garden has a rectangular section that is 30m long and 12m wide and a semi-circular section.1.how much fencing does maria need to fence outside of the hole garden?
I assume she only needs fencing along 3 sides of the rectangle, plus a semicircle on the longer side.
perimeter = 30 + 2(12) + (1/2)(2π(15))
= 54 + 15π
or appr 101.12 m
To find out how much fencing Maria needs to enclose the entire garden, we need to calculate the total perimeter of both sections.
1. Rectangular Section:
The length of the rectangular section is given as 30m, and the width is 12m. To find the perimeter, we use the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
P(rectangular) = 2(30 + 12) = 84m
2. Semi-Circular Section:
The semi-circular section is in the shape of a half-circle. To find the perimeter of a half-circle, we use the formula P(semi-circle) = πr + 2r, where P is the perimeter, π is a mathematical constant (~3.14), and r is the radius. The radius can be calculated by dividing the diameter by 2.
Given that the length of the rectangular section is also the diameter of the semi-circular section (30m), we can find the radius as follows:
r = 30/2 = 15m
P(semi-circle) = π(15) + 2(15) = 47.1m (approx.)
3. Total Fencing:
To find the total fencing needed, we add up the perimeters of the rectangular and semi-circular sections.
Total fencing = P(rectangular) + P(semi-circle) = 84m + 47.1m ≈ 131.1m
Therefore, Maria needs approximately 131.1 meters of fencing to enclose the entire garden.