To determine the area of a garden that is in the shape of a semicircle with a diameter of 38 meters, we will follow these steps:
1. Calculate the radius of the semicircle:
The radius [tex]\( r \)[/tex] of a circle is half of its diameter. Given that the diameter is 38 meters, we calculate the radius as:
[tex]\[
r = \frac{38}{2} = 19 \text{ meters}
\][/tex]
2. Calculate the area of the full circle:
The area [tex]\( A \)[/tex] of a full circle is given by the formula:
[tex]\[
A = \pi r^2
\][/tex]
Substituting the given value of [tex]\(\pi = 3.14\)[/tex] and the calculated radius [tex]\( r = 19 \)[/tex]:
[tex]\[
A = 3.14 \times (19)^2 = 3.14 \times 361 = 1133.54 \text{ square meters}
\][/tex]
3. Calculate the area of the semicircle:
A semicircle is half of a full circle. Therefore, the area of the semicircle is:
[tex]\[
\text{Area of semicircle} = \frac{1133.54}{2} = 566.77 \text{ square meters}
\][/tex]
4. Round the result to the nearest tenth:
The area of the semicircle, rounded to the nearest tenth, is:
[tex]\[
566.8 \text{ square meters}
\][/tex]
Therefore, the area of the garden rounded to the nearest tenth is:
Answer: 566.8
