If the perimeter of a sector of a circle of radius 6.5 cm is 29 cm, then its area is _________

To find the area of a sector of a circle, we first need to find the angle of the sector.

Step 1: Find the circumference of the entire circle. The formula for the circumference of a circle is 2πr, where r is the radius of the circle.

Circumference = 2πr = 2π(6.5 cm) = 13π cm

Step 2: Find the length of the arc of the sector. The perimeter of the sector is the sum of the radius, radius, and the arc length. So, the arc length is the perimeter minus twice the radius.

Arc length = Perimeter - 2r = 29 cm - 2(6.5 cm) = 16 cm

Step 3: Find the angle of the sector. The ratio of the arc length to the circumference of the circle is equal to the ratio of the angle of the sector to 360 degrees.

Angle = (Arc length / Circumference) * 360 = (16 cm / 13π cm) * 360 ≈ 140.74 degrees

Step 4: Find the area of the sector. The ratio of the angle of the sector to 360 degrees is equal to the ratio of the area of the sector to the area of the circle. The area of a circle is πr².

Area of sector = (Angle / 360) * πr² = (140.74 / 360) * π(6.5 cm)² ≈ 33.18 cm²

So, the area of the sector is approximately 33.18 cm².