В трапеции ABCD известно, что AD = 4, BC = 2. Найдите площадь трапеции, если площадь треугольника ABC равна 30.

To find the area of the trapezoid, we can use the formula:

Area = (Sum of the lengths of the bases) * (Height) / 2

In this case, the bases are AD and BC, and we are given that AD = 4 and BC = 2.

So the sum of the lengths of the bases is 4 + 2 = 6.

We are also given that the area of triangle ABC is 30, and the height of the trapezoid is the same as the height of the triangle.

Substituting the values into the formula, we have:

Area = (6) * (Height) / 2

Since the area of triangle ABC is equal to the area of the trapezoid, we have:

30 = (6) * (Height) / 2

To solve for the height, we can multiply both sides of the equation by 2 and divide by 6:

Height = (30 * 2) / 6

Simplifying, we get:

Height = 10

Now we can substitute the values of the bases AD and BC, and the height into the formula for the area of the trapezoid:

Area = (4 + 2) * 10 / 2 Area = 6 * 10 / 2 Area = 60 / 2 Area = 30

So the area of the trapezoid is 30.