Question

Диоганаль BD паралелограмма ABCD перпендикулярна к стороне AD , AB = 12 см угол A =60 градусов найти площадь паралелограмма

Answer 1

12/sin90= x/sin 30

x=6

S- 12*6sin 60= 36 корнеь из 3

Answer 2

Given Information

We are given that the diagonal BD of parallelogram ABCD is perpendicular to side AD, AB = 12 cm, and angle A = 60 degrees. We need to find the area of the parallelogram.

Solution

To find the area of the parallelogram, we can use the formula: Area = base × height.

Finding the Base

The base of the parallelogram is the length of side AB. Given that AB = 12 cm, we can use this as the base.

Finding the Height

To find the height of the parallelogram, we need to find the length of the perpendicular from side AD to the diagonal BD. Since BD is perpendicular to AD, the height is the length of the perpendicular segment.

To find the length of the perpendicular segment, we can use trigonometry. Since angle A is 60 degrees, we can use the sine function to find the length of the perpendicular segment.

Let's denote the length of the perpendicular segment as h.

Using the sine function: sin(A) = opposite/hypotenuse

In this case, the opposite side is the length of the perpendicular segment (h), and the hypotenuse is the length of side AB (12 cm).

sin(60 degrees) = h/12

Simplifying the equation, we have:

h = 12 × sin(60 degrees)

Now, we can calculate the value of h.

Calculation

Using a calculator, we find that sin(60 degrees) is equal to √3/2.

Substituting this value into the equation, we have:

h = 12 × (√3/2)

Simplifying further, we get:

h = 6√3 cm

Finding the Area

Now that we have the base (AB = 12 cm) and the height (h = 6√3 cm), we can calculate the area of the parallelogram using the formula: Area = base × height.

Area = 12 cm × 6√3 cm

Simplifying the expression, we have:

Area = 72√3 cm²

Therefore, the area of the parallelogram ABCD is 72√3 cm².

Answer

The area of the parallelogram ABCD is 72√3 cm².