Question

find the area of the semicircle. either enter an exact answer in terms of \\(\pi\\) or use 3.14 for \\(\pi\\) and enter your answer as a decimal. \\(\square\\) units\\(^2\\) show calculator

Explanation:

Step1: Identify radius of semicircle

The diameter is 6, so radius $r = \frac{6}{2} = 3$.

Step2: Use semicircle area formula

The area of a full circle is $\pi r^2$, so semicircle area is $\frac{1}{2} \pi r^2$. Substitute $r=3$:
$\frac{1}{2} \pi (3)^2 = \frac{1}{2} \pi \times 9 = \frac{9}{2}\pi$

Step3: Calculate decimal value (optional)

Substitute $\pi=3.14$:
$\frac{9}{2} \times 3.14 = 4.5 \times 3.14 = 14.13$

Answer:

Exact answer: $\frac{9}{2}\pi$ units$^2$
Decimal answer: $14.13$ units$^2$