If the arc length is 20π, the circumference of the cone bottom is 20π, the radius of the bottom is 20π divided by 2π= 10, and the square of the bottom area is 10 π= 100π.

Lateral area is a fan-shaped area, the fan-shaped radius is set to X, the arc length =( 150 degrees/180 degrees) πx=20π, so the fan-shaped radius is 24, and the fan-shaped area is equivalent to the whole circle area of (150/360) radius 24, which is 24 * 24.

The total area is 100π+240π=340π.