The radii of the bases of the truncated cone are 6 cm and 10 cm, and the generatrix is 10 cm. Find the surface of the axial section.

At the base of the truncated cone is an isosceles trapezoid. The bases of the trapezoid are 12 cm and 20 cm (2 radii), the lateral side is 10 cm (it is also generating).
The area of the trapezoid is found by the formula: half the sum of the bases * per height. The half-sum of the bases is = 1/2 * (12 + 20) = 16 (cm)
Let’s find the height. It is equal to the square root of (generating squared – the difference of radii squared) = √ (100 – 16) = √ (84) = 2 * √ (21).
Area = 16 * 2 * √ (21) = 32 * √ (21) (square cm)
Answer: 32 * √21.