Find the area of the minor segment in a circle with radius 6.2 cm and subtending an angle of 135 degrees at the centre.

To find the area of the minor segment of a circle, you will need to find the area of the corresponding sector and subtract the area of the triangle formed by the two radii and the chord.

Step 1: Find the area of the sector
The area of a sector can be calculated using the formula:
Area of sector = (angle/360) * π * r^2
where angle is the measure of the angle in degrees and r is the radius.

In this case, the angle is given as 135 degrees and the radius is 6.2 cm. Plugging the values into the formula:
Area of sector = (135/360) * π * (6.2 cm)^2

Step 2: Find the area of the triangle
To find the area of the triangle, you will need to calculate the base and height of the triangle. The base of the triangle is the length of the chord, which can be found using the formula:
Chord length = 2 * r * sin(angle/2)
where r is the radius and angle is the measure of the angle in degrees.

In this case, the angle is 135 degrees and the radius is 6.2 cm. Plugging the values into the formula:
Chord length = 2 * (6.2 cm) * sin(135/2)

To find the height of the triangle, you can use the formula:
Height = r * cos(angle/2)
where r is the radius and angle is the measure of the angle in degrees.

In this case, the angle is 135 degrees and the radius is 6.2 cm. Plugging the values into the formula:
Height = (6.2 cm) * cos(135/2)

Now, you can calculate the area of the triangle using the formula:
Area of triangle = (1/2) * base * height
where base and height are the values you calculated above.

Step 3: Find the area of the minor segment
To find the area of the minor segment, simply subtract the area of the triangle from the area of the sector.
Area of minor segment = Area of sector - Area of triangle

By following these steps and plugging in the values given in the problem, you will be able to find the area of the minor segment in the circle.