Lesson Worksheet: Area of Circular Segments: Degrees Mathematics

In this worksheet, we will practice finding the area of a circular segment where angles are measured in degrees.

Q1:

Find the area of the colored segment of the circle. Round your answer to three decimal places.

Q2:

Find the area of a circular segment that has a 2 cm radius and a 120 central angle. Round your answer to three decimal places.

Q3:

The area of the shaded region is 20 cm2. Find the length of 𝐴𝑂. Round your answer to two decimal places.

Q4:

In a circle with center 𝑂, 𝐴𝑂𝐵 is a right triangle. If the area of the triangle is 10 cm2, find the area of the shaded region. Round your answer to three decimal places.

Q5:

Find the shaded area.

Q6:

A square with side length 20 cm contains two-quarters of two identical circles with centers 𝐴 and 𝐶. Find the area of the shaded region. Round your answer to two decimal places.

Q7:

𝐴𝐵𝐶 is a right triangle in a quarter of a circle with center 𝐶, where 𝐴𝐶 and 𝐵𝐶 are both radii. 𝐴𝐵 is a diameter in a circle with center 𝑀. Find the area of the shaded region given that 𝐴𝐶=5cm.

Q8:

𝐴𝐵 is a chord in a circle with center 𝑂 and diameter 20 cm. If 𝑚𝐴𝑂𝐵=30, find the area of the major segment 𝐴𝐵 to the nearest decimal place.

Q9:

Two circles with centers 𝐵 and 𝐸 touch from outside. 𝐴𝐵=10cm and 𝐷𝐸=7cm, while the measures of 𝐴𝐵𝐶=62 and 𝐷𝐸𝐹=70. Find the area of the shaded region. Round your answer to two decimal places.

Q10:

A circle of center 𝑀 has a radius of 13 cm, 𝑀𝐶𝐴𝐵, and 𝑀𝐶=6cm. Find the central angle of the minor circular segment 𝐴𝐷𝐵 giving the answer to the nearest second.

  • A125138
  • B244631
  • C623049
  • D49331

This lesson includes 1 additional question and 63 additional question variations for subscribers.

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