The area of a sector of a circle is given by the formula:
A = (θ/360) × πr^2
where θ is the central angle of the sector in degrees, r is the radius of the circle, and π is the mathematical constant pi.
In this case, the radius of the circle is given as 5 centimeters, and the central angle of the sector is 90°. Substituting these values into the formula, we get:
A = (90/360) × π(5)^2
A = (1/4) × 25π
A = (25/4)π
The exact area of the sector in simplest form is (25/4)π square centimeters.