Question

В равнобедренной трапеции основания равны 2 и 6 см а один из углов между боковой стороной 45 градусов найдите площадь трапеции

Answer 1

1) Проведем высоты ВН и СН1 к большему  основанию AD. ВС=НН1=2 см.
2) ∆АВН=∆Н1СD (по гипотенузе и катету), значит, АН=Н1D.
3) AD=2*АН+НН1
   6=2*АН+2
   АН=2 
4) В прямоугольном ∆АВН угол А=45, значит, АН=ВН=2 см.
5) Sabcd=1/2*BH*(BC+AD)=1/2*2*(2+6)=8 см^2
Ответ: 8 см^2.

Answer 2

Calculation of the Trapezoid Area

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

Area = (a + b) * h / 2

where: - a and b are the lengths of the parallel bases of the trapezoid, and - h is the height of the trapezoid, which is the perpendicular distance between the bases.

In this case, the lengths of the bases are given as 2 cm and 6 cm, and the angle between one of the lateral sides and the base is 45 degrees.

Let's calculate the area using the formula:

Area = (2 + 6) * h / 2

To find the height, we can use trigonometry. Since we have a right triangle formed by the height, the base, and the lateral side, we can use the cosine function:

cos(45) = base / hypotenuse

In this case, the base is the height of the trapezoid, and the hypotenuse is the lateral side.

Let's calculate the height using the cosine function:

cos(45) = h / 6

Simplifying the equation:

h = 6 * cos(45)

Now we can substitute the value of the height into the area formula:

Area = (2 + 6) * (6 * cos(45)) / 2

Calculating the area:

Area = (8) * (6 * cos(45)) / 2

Area = 24 * cos(45)

Using a calculator, we find that cos(45) = 0.7071.

Substituting the value of cos(45) into the equation:

Area = 24 * 0.7071

Area = 16.9704 cm²

Therefore, the area of the trapezoid is approximately 16.9704 cm².

Answer

The area of the trapezoid with bases measuring 2 cm and 6 cm, and an angle of 45 degrees between one of the lateral sides and the base, is approximately 16.9704 cm².