a chord of radius 20cm subtends an angle of 90 degrees at centre. find the area of the corresponding major segment of the circle

Make a sketch, drawing the right-angled triangle formed by the chord and the two radii.

Find the area of that triangle, very easy
find the area of the 1/4 of the circle, very easy
subtract those two to get the minor segment
Find the area of the whole circle and subtract the minor segment from that.

To find the area of the corresponding major segment, we need to find the area of the entire circle and deduct the area of the minor sector formed by the given angle.

First, let's find the area of the entire circle. The formula for the area of a circle is given by A = πr², where A represents the area and r represents the radius.

In this case, the radius is given as 20 cm. So, the area of the entire circle is:

A = π * (20 cm)²
A = π * 400 cm²
A = 400π cm² (approx. 1256.64 cm²)

Now, let's calculate the area of the minor sector formed by the given angle. The formula for the area of a sector is given by A = (θ/360) * πr², where θ represents the angle in degrees and r represents the radius.

In this case, the angle is given as 90 degrees and the radius is given as 20 cm. So, the area of the minor sector is:

A = (90/360) * π * (20 cm)²
A = (1/4) * π * 400 cm²
A = 100π cm² (approx. 314.16 cm²)

Finally, to find the area of the major segment, subtract the area of the minor sector from the area of the entire circle:

Area of Major Segment = Area of entire circle - Area of minor sector
Area of Major Segment = 400π cm² - 100π cm²
Area of Major Segment = 300π cm² (approx. 942.48 cm²)

Therefore, the area of the corresponding major segment of the circle is 300π cm² (approximately 942.48 cm²).