The area of the trapezoid is 288 cm ^ 2 of the base, refer to 4 ÷ 5 height 3.2 dm calculate the base.

Consider the formula for the area of ​​a trapezoid
From the condition of the problem, we know that the area of ​​the considered trapezoid is 288 cm2. We also know that the area of ​​a trapezoid is calculated as the product of the half-sum of the bases and the height. That is, the formula will look like this:

S = 1/2 * (a + b) * h

Where:

S is the area of ​​the trapezoid;
a – smaller base of the trapezoid;
b – correspondingly larger base of the trapezoid;
h – height.
From the condition of the problem, we know that the area of ​​the trapezoid is S = 288 cm2, and the height is h = 3.2 dm.

Let us bring these quantities to a single measurement system, that is, we translate decimeters into centimeters:

1 dm = 10 cm => 3.2 dm = 32 cm

Then our formula will take the following form:

S = 1/2 * (a + b) * h;

288 = 1/2 * (a + b) * 32;

288/32 = 1/2 * (a + b);

9 / 1/2 = a + b;

a + b = 9 * 2;

a + b = 18

That is, we got that the sum of the lengths of the bases of the considered trapezoid is 18 cm.

Also, from the problem statement, we know that the lengths of the bases are related as 4: 5. That is, we can write the following:

a: b = 4: 5

By the rule of proportion, we know that the product of the extreme terms is equal to the product of its middle terms. Thus, we can write that:

5 * a = 4 * b

Therefore, we get a system of simple linear equations with two unknowns:

a + b = 18

5 * a = 4 * b

Let’s solve the system of equations
Let us express a from the first equation of our system and substitute the resulting value into the second equation. Thus, we get:

a = 18 – b

Then

5 * (18 – b) = 4 * b;

90 – 5 * b = 4 * b;

4 * b + 5 * b = 90;

b * (4 + 5) = 90;

9 * b = 90;

b = 90/9 = 10

That is, the length of the larger base is b = 10 cm.

Then the smaller base: a = 18 – b = 18 – 10 = 8 cm.

Answer: 8 cm, 10 cm