The arc of a sector measures 90 degrees. The length of the radius is 7 cm. Find the area of the segment bounded by the arc and the corresponding chord.

Sure, here are the steps to find the area of the segment:

1. First, we need to find the area of the sector. The formula for the area of a sector is (θ/360) * π * r², where θ is the angle of the sector and r is the radius. In this case, θ is 90 degrees and r is 7 cm. So, the area of the sector is (90/360) * π * 7² = 38.5 cm².

2. Next, we need to find the area of the triangle formed by the radius and the chord. This is a right triangle because the angle of the sector is 90 degrees. The formula for the area of a triangle is 1/2 * base * height. In this case, the base and the height are both the radius, which is 7 cm. So, the area of the triangle is 1/2 * 7 * 7 = 24.5 cm².

3. Finally, we subtract the area of the triangle from the area of the sector to find the area of the segment. So, the area of the segment is 38.5 - 24.5 = 14 cm².