Question

Дана трапеция АВСД.Основания трапеции относятся,как 2:1.Площадь треугольника АВС равна 8см.кв.Найти площадь трапеции АВСД. Пишу задачу на работе и,поэтому,не совсем уверена ,что полностью озвучила условие задачи.По-моему,все. Элона

Answer 1

а-малое основание

в-большое основание

с-высота

SΔ=0.5*с*в

Sтр=0,5*с*(а+в)

пусть а=х, тогда в=2*х

с=8/х

Sтр=0,5*8/х*(х+2*х)=12

Answer 2

Finding the Area of Trapezoid ABCD

To find the area of trapezoid ABCD, we can use the given information about the trapezoid and the triangle ABC.

Given: - Bases of the trapezoid are in a 2:1 ratio. - Area of triangle ABC is 8 square centimeters.

Solution

Let's denote the lengths of the bases of the trapezoid as follows: - Larger base: B - Smaller base: b

The area of a trapezoid can be calculated using the formula: Area = (1/2) * (sum of the lengths of the parallel sides) * (height)

We know that the bases of the trapezoid are in a 2:1 ratio. Let's assume the lengths of the bases are 2x and x, where x is a positive real number.

Given that the area of triangle ABC is 8 square centimeters, we can use this information to find the height of the trapezoid.

The area of a triangle can be calculated using the formula: Area = (1/2) * (base) * (height)

We are given the area of triangle ABC as 8 square centimeters, and the base of this triangle is the difference between the larger and smaller bases of the trapezoid, which is B - b.

Using the given information, we can solve for the height of the trapezoid and then use it to find the area of trapezoid ABCD.

Calculation

Let's denote the height of the trapezoid as h.

The area of triangle ABC is given as 8 square centimeters: 8 = (1/2) * (B - b) * h

We also know that the bases of the trapezoid are in a 2:1 ratio: B = 2b

Substituting B = 2b into the area equation, we get: 8 = (1/2) * (2b - b) * h 8 = (1/2) * b * h 16 = b * h

Now, we need to find the area of trapezoid ABCD using the formula: Area = (1/2) * (B + b) * h

Substitute B = 2b into the area formula: Area = (1/2) * (2b + b) * h Area = (1/2) * 3b * h Area = (3/2) * b * h

We already found that b * h = 16, so: Area = (3/2) * 16 Area = 24 square centimeters

Conclusion

The area of trapezoid ABCD is 24 square centimeters.