The perimeter of the sector of the circle is determined to be 28.428 cm.
The area of the sector is given as 40 cm² and the radius of the given circle is mentioned as 7 cm.
In order to calculate the perimeter we need to find the value of the angle of the sector and the arc length as well.
∴ Area of the sector = angle of the sector/ 360° × πr²
⇒ 40 = x/360° × 22/7 × (7)²
⇒x = 40 × 360/ 22 × 7
⇒x = 93.506°
Arc length = angle of the sector/360° × π × 2 × r
Arc length = 93.506°/360° × 22/7 × 2 × 7 = 11.428 cm
∴ Perimeter = arc length + radius +radius
Perimeter = 11.428 + 7 + 7 = 28.428 cm