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The area of the segment of a circle is determined by subtracting the triangle formed inside the sector from the sector which has the segment. In this article, we shall discuss in detail the segment and area of a segment of a circle and all related theorems with proof.
To work out the area of a segment we can use the formula for the area of a triangle and the formula for the area of a sector. We subtract the area of the triangle from the area of the sector. The formula for the area of a triangle is. \text { Area of a triangle }=\cfrac {\text { base } \times \text { height }} {2}.
What Is the Formula for Area of the Segment of a Circle? The area of the segment of the circle (or) minor segment of a circle is: (θ / 360°) × πr 2 - (1/2) r 2 sin θ (OR) r 2 [πθ/360° - sin θ/2], if 'θ' is in degrees
Area of Segment. The Area of a Segment is the area of a sector minus the triangular piece (shown in light blue here). There is a lengthy reason, but the result is a slight modification of the Sector formula: Area of Segment = θ − sin (θ)2 × r 2 (when θ is in radians)
Work out the area of the shaded segment. Give your answer to 1 decimal place.....cm² (5) © Corbettmaths 2022
You can calculate the segment area in three steps: Determine the radius of the circle. Calculate the central angle. Apply the segment area formula: 0.5 × r² × (α – sin(α))
A segment of a circle is the area enclosed by an arc of a circle and a chord. There are two main types of segment: The major segment is the segment where the arc length is greater than half the circumference of the circle. The minor segment is the segment where the arc length is less than half the circumference of the circle.
