Question

Острый угол прямоугольной трапеции АВСD равен 30 градусов. Сумма длин её боковых сторон равна 12 корней из 3 см, меньшее основание ВС равно 8 см. вычислить площадь трапеции. ПОМОГИТЕ ПЖ СРОЧНОТОЛЬКО НАДО С ДАНО И ВСЕЙ ФИГНЁЙ

Answer 1

Проведём высоту СН. CH=AB.
В прямоугольном треугольнике СНD 
CH=CD*sin∠D=0.5CD
AB+CD=CH+CD=1.5CD=12√3
CD=8√3, CH=4√3,
HD=CD*cos∠D=8√3 * 0.5√3=12.
ABCH - прямоугольник, AH=BC=8,
AD=AH+HD=8+12=20.
S=0.5(BC+AD)*CH=0.5*(8+20)*4√3=56√3 (см²).
Ответ. S = 56√3 см²

Answer 2

Given Information:

We are given the following information about the trapezoid ABCD: - The acute angle of the trapezoid, ∠ABC, is 30 degrees. - The sum of the lengths of its lateral sides is 12√3 cm. - The length of the smaller base, BC, is 8 cm.

Solution:

To find the area of the trapezoid, we need to know the lengths of both bases. However, we are only given the length of the smaller base, BC. To find the length of the larger base, AD, we can use the fact that the sum of the lengths of the lateral sides is equal to the sum of the lengths of the bases.

Let's denote the length of the larger base, AD, as x cm. Then we have the following equation:

BC + AD = 12√3 cm

Substituting the given values, we have:

8 cm + x cm = 12√3 cm

To solve for x, we can subtract 8 cm from both sides of the equation:

x cm = 12√3 cm - 8 cm

Simplifying the equation, we have:

x cm = 12√3 cm - 8 cm x cm = 4(3√3 - 2) cm

Now that we have the lengths of both bases, we can calculate the area of the trapezoid using the formula:

Area = (BC + AD) * h / 2

where h is the height of the trapezoid. Since the height is not given, we cannot calculate the exact area of the trapezoid without additional information.

Please provide the height of the trapezoid, and I will be able to calculate the area for you.