Question

основания равнобедренной трапеции равны 8 и 14, а тангенс угла при одном из оснований равен 4/3. найдите ее площадь. :)

Answer 1

Назовём трапецию ABCD(AB-меньшее основание) Опустим высоты AH  и ВP. HP=AB т.к. ABPH прямоугольник. Т.к. СD=HP+CP+DH то СP=DH=(CD-AB)/2=3

Если катет прилежит к большему основанию то высота AH=9/4=2.25 А площадь равна 

2.25*11=24.75

Если к меньшему то AH=4 а площадь 4*11=44

Answer 2

Опускаем высоту из вершины

Ищем эту высоту через тангенс

tg=h/a

а - это часть основания ((14-8)/2=3)

h=(4\3)*3=4

S=1/2*(a+b)*h=1/2*22*4=44

Ответ: 44

Answer 3

Finding the Area of an Isosceles Trapezoid

To find the area of an isosceles trapezoid, we need to know the lengths of the bases and the height. In this case, we are given that the lengths of the bases are 8 and 14, and the tangent of one of the angles is 4/3.

Let's denote the length of the shorter base as a (which is 8) and the length of the longer base as b (which is 14). We also need to find the height of the trapezoid.

To find the height, we can use the formula for the tangent of an angle in a right triangle. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the trapezoid, and the adjacent side is half the difference between the lengths of the bases.

Let's denote the height of the trapezoid as h. We can set up the following equation:

tan(angle) = h / ((b - a) / 2)

Substituting the given values, we have:

4/3 = h / ((14 - 8) / 2)

Simplifying the equation, we get:

4/3 = h / 3

Cross-multiplying, we have:

4 * 3 = h * 3

12 = h * 3

Dividing both sides by 3, we find:

h = 4

Now that we have the height of the trapezoid, we can calculate its area using the formula:

Area = (a + b) * h / 2

Substituting the given values, we have:

Area = (8 + 14) * 4 / 2

Simplifying the equation, we get:

Area = 22 * 4 / 2

Area = 44

Therefore, the area of the isosceles trapezoid is 44 square units.

Please let me know if you have any further questions!