A circle is a curve sketched out by a point moving in a plane. The area of the sector of the circle is 19.625 units².
What is a circle?
A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
Given the length of OA is 5 units, therefore, the radius of the circle is 5 units. Also, it is given that the ratio of the length of AB and the circumference of the circle is 1/4. Thus, we can write,
Length of AB = Circumference of the circle × (θ/360°)
Length of AB/ circumference of the circle = (θ/360°) = 1/4
(θ/360°) = 1/4
θ = 90°
Hence, the measure of the central angle is 90°.
The area of the sector is,
Area of sector= Area of the circle × (θ/360°)
Area of sector= π× R² × (90°/360°)
Area of sector = 3.14 × 5² × 0.25 = 19.625 units²
Hence, the area of the sector of the circle is 19.625 units².
Learn more about Circle:
https://brainly.com/question/11833983
#SPJ5
