Question

find the area of the semicircle. either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal. units²

Explanation:

Step1: Recall full circle area formula

The area of a full circle is $A = \pi r^2$, where $r=6$.

Step2: Calculate full circle area

$A_{\text{full}} = \pi \times 6^2 = 36\pi$

Step3: Find semicircle area (half full area)

$A_{\text{semicircle}} = \frac{1}{2} \times A_{\text{full}}$
$A_{\text{semicircle}} = \frac{1}{2} \times 36\pi = 18\pi$

Step4: (Optional) Decimal approximation

Using $\pi=3.14$:
$A_{\text{semicircle}} = 18 \times 3.14 = 56.52$

Answer:

Exact answer: $18\pi$ units$^2$
Decimal approximation: $56.52$ units$^2$