If the perimeter of a sector of a circle of radius 6.5 cm is 29 cm, then its area is _________52 cm258 cm254 cm256 cm2

The problem is asking for the area of a sector of a circle. The steps to solve this problem are as follows:

Step 1: The perimeter of a sector is given by the formula P = 2πr + 2rθ, where r is the radius and θ is the angle of the sector in radians. We know that the perimeter P is 29 cm and the radius r is 6.5 cm. We can use these values to solve for θ.

Step 2: Substitute the given values into the formula: 29 = 2π(6.5) + 2(6.5)θ. Simplify the equation to find the value of θ.

Step 3: The area of a sector is given by the formula A = 0.5r²θ. Once you have found the value of θ from Step 2, substitute the values of r and θ into this formula to find the area of the sector.

Step 4: The possible answers given are 52 cm², 258 cm², 254 cm², and 256 cm². Compare your calculated area from Step 3 to these options to find the correct answer.