The height and base of the trapezoid are 5: 6: 4 find the smaller base if s = 81 cm2.

Let’s solve this problem using the equation.

Let the length of the smaller base be 4 * x centimeters, then the length of the larger base is 6 * x centimeters, and the length of the height is 5 * x centimeters. We know that the area of the trapezoid is 81 cm2. Let’s make the equation:

1/2 * (6 * x + 4 * x) * 5 * x = 81;

(6 * x + 4 * x) * 5 * x = 81 * 2;

(6 * x + 4 * x) * 5 * x = 162;

10 * x * 5 * x = 162;

50 * x ^ 2 = 162 (in order to find an unknown factor, you need to divide the product by a known factor);

x ^ 2 = 162: 50;

x ^ 2 = 3.24;

x = 1.8 centimeters;

4 * 1.8 = 7.2 centimeters – the length of the smaller base.

Answer: 7.2 centimeters.