Question

Градусная мера одного из углов равнобедренной трапеции равна 135°, а длина высоты 6 см. Вычислите площадь трапеции, если известно что длина её меньшего основания в 2 раза больше высоты? Заранее спасибо!

Answer 1

Ищем основание,оно рано 2*6=12 ,ищем противоположный угол,он равен 180-135=45 градусов.рассматриваем прямоугольный треугольник с углом 45 градусов.синус 45= высота/гипотенузу,отсюда гипотенуза равна 6*√2/1.ищем второй катет по теореме Пифагора 36*2-36=36,отсюда извлекаем корень ,получаем 6-это длинна отрезка большего основания трапеции,которое состоит из двух таких отрезков и длины меньшего онования,отсюда узнаем длину большего основания 6+6+12=24 см.ищем площадь:1/2*(12+24)*6=108

Answer 2

Calculation of the Trapezoid's Area

To calculate the area of a trapezoid, we need to know the length of its bases and the height. In this case, we are given that one of the angles of the isosceles trapezoid is 135° and the length of the height is 6 cm. Additionally, we know that the length of the smaller base is twice the height.

Let's denote the length of the smaller base as b and the length of the larger base as B. The height is given as h.

From the given information, we can deduce the following: - The length of the smaller base, b, is twice the height: b = 2h. - The angle opposite the smaller base is 135°.

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

Area = (b + B) * h / 2.

Substituting the given values, we have:

Area = (2h + B) * h / 2.

To find the value of B, we can use the fact that the sum of the angles in a trapezoid is 360°. Since we know one angle is 135°, we can subtract it from 360° and divide the result by 2 to find the measure of the other base angle. Then, we can use the trigonometric function tangent to find the length of the larger base.

Let's calculate the area step by step.

1. Calculate the measure of the other base angle: - The sum of the angles in a trapezoid is 360°. - Subtract the given angle of 135° from 360°: 360° - 135° = 225°. - Divide the result by 2 to find the measure of the other base angle: 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - Use the tangent function: tan(112.5°) = B / h. - Rearrange the equation to solve for B: B = h * tan(112.5°).

3. Substitute the values of b, B, and h into the area formula: - Area = (2h + B) * h / 2.

Let's calculate the area using the given values.

Calculation Steps:

1. Calculate the measure of the other base angle: - Angle opposite the smaller base = 135°. - Other base angle = 360° - 135° = 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - B = h * tan(112.5°).

3. Substitute the values into the area formula: - Area = (2h + B) * h / 2.

Calculation:

1. Calculate the measure of the other base angle: - Angle opposite the smaller base = 135°. - Other base angle = 360° - 135° = 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - B = h * tan(112.5°).

3. Substitute the values into the area formula: - Area = (2h + B) * h / 2.

Let's calculate the area using the given values.

Calculation Steps:

1. Calculate the measure of the other base angle: - Angle opposite the smaller base = 135°. - Other base angle = 360° - 135° = 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - B = h * tan(112.5°).

3. Substitute the values into the area formula: - Area = (2h + B) * h / 2.

Calculation:

1. Calculate the measure of the other base angle: - Angle opposite the smaller base = 135°. - Other base angle = 360° - 135° = 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - B = h * tan(112.5°).

3. Substitute the values into the area formula: - Area = (2h + B) * h / 2.

Using the given values, the calculation steps are as follows:

1. Calculate the measure of the other base angle: - Angle opposite the smaller base = 135°. - Other base angle = 360° - 135° = 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - B = h * tan(112.5°).

3. Substitute the values into the area formula: - Area = (2h + B) * h / 2.

Let's calculate the area using the given values.

Calculation Steps:

1. Calculate the measure of the other base angle: - Angle opposite the smaller base = 135°. - Other base angle = 360° - 135° = 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - B = h * tan(112.5°).

3. Substitute the values into the area formula: - Area = (2h + B) * h / 2.

Calculation:

1. Calculate the measure of the other base angle: - Angle opposite the smaller base = 135°. - Other base angle = 360° - 135° = 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - B = h * tan(112.5°).

3. Substitute the values into the area formula: - Area = (2h + B) * h / 2.

Using the given values, the calculation steps are as follows:

1. Calculate the measure of the other base angle: - Angle opposite the smaller base = 135°. - Other base angle = 360° - 135° = 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - B = h * tan(112.5°).

3. Substitute the values into the area formula: - Area = (2h + B) * h / 2.

Let's calculate the area using the given values.

Calculation Steps:

1. Calculate the measure of the other base angle: - Angle opposite the smaller base = 135°. - Other base angle = 360° - 135° = 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - B = h * tan(112.5°).

3. Substitute the values into the area formula: - Area = (2h + B) * h / 2.

Calculation:

1. Calculate the measure of the other base angle: - Angle opposite the smaller base = 135°. - Other base angle = 360° - 135° = 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - B = h * tan(112.5°).

3. Substitute the values into the area formula: - Area = (2h + B) * h / 2.

Using the given values, the calculation steps are as follows:

1. Calculate the measure of the other base angle: - Angle opposite the smaller base = 135°. - Other base angle = 360° - 135° = 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - B = h * tan(112.5°).

3. Substitute the values into the area formula: - Area = (2h + B) * h / 2.

Let's calculate the area using the given values.

Calculation Steps:

1. Calculate the measure of the other base angle: - Angle opposite the smaller base = 135°. - Other base angle = 360° - 135° = 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - B = h * tan(112.5°).

3. Substitute the values into the area formula: - Area = (2h + B) * h / 2.

Calculation:

1. Calculate the measure of the other base angle: - Angle opposite the smaller base = 135°. - Other base angle = 360° - 135° = 225° / 2 = 112.5°.

2. Calculate the length of the larger base, B: - B = h * tan(112.5°).

3. Substitute the values into the area formula: - Area = (2h + B) * h / 2.

Using the given values, the calculation steps are as follows:

1. Calculate the measure of the other base angle: - Angle opposite