The sides of the bases of a regular triangular truncated pyramid are 3 and 9 cm, the lateral surface area

The sides of the bases of a regular triangular truncated pyramid are 3 and 9 cm, the lateral surface area is 36 to find the height of the truncated pyramid.

1. The side face is a trapezoid S = 12, but it is worth noting that there are three of them.
Find S trapezoid by the formula, S = half-sum of bases * h.
Substitute in the formula and solve:
S = (3 + 9) / 2 * H;
S = 12, it is worth noting that then we get H = 2 cm.
2. Let’s use the Pythagorean theorem:
S (ADB) = S (ADC) = (1/2) * 15 * 9;
S (ADB) = S (ADC) = (1/2) * 135;
S (ADB) = S (ADC) = 67.5.