Class 10 Sector and Segment Area: Formulas and Example

Mark the boundaries before calculating

In a minor sector with an angle below 180°, joining the radius endpoints makes a triangle inside the sector. Removing that triangle leaves the minor segment. The diagram uses a right angle so the triangle area is particularly easy.

Keep area and length separate

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Work through a quarter-circle

For radius 14 cm and central angle 90°, the sector is one quarter of the circle. Using π = 22/7 gives sector area 154 cm². The triangle enclosed by the two radii is right-angled, with area ½ × 14 × 14 = 98 cm². The minor segment therefore has area 56 cm².

The arc length is 22 cm. The sector perimeter is 22 + 14 + 14 = 50 cm. Neither 22 nor 50 is an area. For the segment perimeter, replace the two radii with the chord length, which here is 14√2 cm; the result is 22 + 14√2 cm.

Check a shaded-region answer

A minor segment must have less area than its enclosing minor sector. Use the value of π requested by the question and keep exact expressions until the final step when none is specified. For a major region, subtract the corresponding minor region from the full circle.

When a diagram combines several shapes, write a sentence such as “quarter-circle minus right triangle” before a formula. If that sentence does not describe the shaded boundaries, the arithmetic will solve a different problem.

Choose what to study next

Sources and scope

This is a focused learning resource, not a complete chapter or a prediction of board questions. Use your current syllabus and the paper-specific marking scheme for assessment requirements.