Final answer:
The area of the circle with a circumference of 13π cm is 42.25π cm² when expressed in terms of π.
Step-by-step explanation:
To find the area of the circle given the circumference, first retrieve the radius from the circumference. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Given that the circumference C is 13π cm, we can set up the equation 13π cm = 2πr to find the radius r.
Solving for r gives us:
r = ½ × 13 cm = 6.5 cm
Now, use the radius to calculate the area A using the formula for the area of a circle, A = πr².
Substituting our value for r, we get:
A = π × (6.5 cm)² = π × 42.25 cm² = 42.25π cm².
Thus, the area of the circle, expressed in square centimetres in terms of π, is 42.25π cm².