To find the area of a circle, you can use the formula:
\[ \text{Area} = \pi r^2 \]
where \( r \) is the radius of the circle.
In this case, the diameter of the circle is given as 84 cm. The radius (\( r \)) is half of the diameter:
\[ r = \frac{diameter}{2} = \frac{84 , \text{cm}}{2} = 42 , \text{cm} \]
Now, substitute \( r \) into the area formula using \( \pi \approx 3.14 \):
\[ \text{Area} = 3.14 \times (42 , \text{cm})^2 \]
First, calculate \( (42 , \text{cm})^2 \):
\[ (42)^2 = 1764 , \text{cm}^2 \]
Now, multiply this by 3.14:
\[ \text{Area} = 3.14 \times 1764 , \text{cm}^2 \]
Calculating this gives:
\[ \text{Area} = 5546.76 , \text{cm}^2 \]
Finally, round to the nearest hundredth if needed (which it is not in this case since it ends with .76):
The area of the circle is approximately
\[ \text{5546.76 } \text{cm}^2. \]