Question

Вычислите площадь трапеции ABCD c основаниями AD и BC, если AD=20 см, BC= 4 см, AB= 16 см и угол А=30градусов.

Answer 1

1) Опустим из B к AD перпендикуляр (это высота трапеции). AB - гипотенуза. Катет, лежащий против угла 30°, равен половине гипотенузы. Получаем:
16:2 = 8 см
2) S = полусумма оснований на высоту, или:
((20+4)/2)*8 = 12*8 = 96 см² 

Answer 2

Calculation of the Trapezoid's Area

To calculate the area of trapezoid ABCD with bases AD and BC, we can use the formula:

Area = (sum of the bases) * height / 2.

Given the following measurements: - AD = 20 cm - BC = 4 cm - AB = 16 cm - Angle A = 30 degrees

We can proceed with the calculation.

First, let's find the height of the trapezoid. To do this, we can use the formula:

Height = AB * sin(A).

Substituting the given values, we have:

Height = 16 cm * sin(30 degrees) = 16 cm * 0.5 = 8 cm.

Next, we can calculate the area using the formula mentioned earlier:

Area = (AD + BC) * height / 2 = (20 cm + 4 cm) * 8 cm / 2 = 24 cm * 8 cm / 2 = 192 cm² / 2 = 96 cm².

Therefore, the area of trapezoid ABCD is 96 cm².

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