Question

В параллелограмме авсд ав =8 см ад =10 см угол д =30° найти площадь параллелограмма

Answer 1

S=a*b*sin30°
S=8*10*1/2 
S=40см

Answer 2

Calculation of the Area of a Parallelogram

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

In this case, we are given that side AV is 8 cm and side AD is 10 cm. We also know that angle D is 30°.

To find the height of the parallelogram, we can use trigonometry. The height is the perpendicular distance between side AD and side BC.

Let's calculate the height using the given information:

1. We can find the length of side BC using the Law of Cosines. The formula is: BC² = AV² + AC² - 2 × AV × AC × cos(angle A).

Plugging in the values, we get: BC² = 8² + 10² - 2 × 8 × 10 × cos(30°).

Solving this equation, we find: BC ≈ 6.928 cm.

2. Now, we can find the height of the parallelogram by using the formula: height = BC × sin(angle D).

Plugging in the values, we get: height = 6.928 × sin(30°).

Solving this equation, we find: height ≈ 3.464 cm.

3. Finally, we can calculate the area of the parallelogram using the formula: Area = base × height.

Plugging in the values, we get: Area = 8 cm × 3.464 cm.

Solving this equation, we find: Area ≈ 27.712 cm².

Therefore, the approximate area of the parallelogram is 27.712 cm².

Answer

The approximate area of the parallelogram ABCD, given that AV = 8 cm, AD = 10 cm, and angle D = 30°, is 27.712 cm².