Question

знайдіть площу паралелограма діагоналі якого дорівнюють 8 см і 14 см а кут між ними 45 градусів геометрія

Answer 1

Ответ:

28√2 см²

Объяснение:

S=1/2*d1*d2*sin45°

sin45°=√2/2

S=1/2*8*14*√2/2=28√2 см²

Answer 2

Finding the Area of a Parallelogram

To find the area of a parallelogram, we can use the formula: Area = base × height. In this case, the base is the length of one of the sides of the parallelogram, and the height is the perpendicular distance between the base and the opposite side.

Given that the diagonals of the parallelogram are 8 cm and 14 cm, and the angle between them is 45 degrees, we can use trigonometry to find the base and height of the parallelogram.

Finding the Base and Height

Let's consider the diagonal of length 8 cm. We can divide it into two equal parts, each forming a right triangle with the base of the parallelogram. The angle between the diagonal and the base is 45 degrees.

Using trigonometry, we can find the length of the base of the parallelogram:

cos(45 degrees) = base / (8 cm / 2)

Simplifying the equation, we have:

base = (8 cm / 2) × cos(45 degrees)

Similarly, we can find the length of the height of the parallelogram using the diagonal of length 14 cm:

height = (14 cm / 2) × cos(45 degrees)

Calculating the Area

Now that we have the base and height of the parallelogram, we can calculate its area using the formula mentioned earlier:

Area = base × height

Let's substitute the values we found:

Area = (8 cm / 2) × cos(45 degrees) × (14 cm / 2) × cos(45 degrees)

Simplifying the equation, we have:

Area = (8 cm × 14 cm / 4) × cos^2(45 degrees)

Area = (112 cm^2 / 4) × 0.5

Area = 28 cm^2 × 0.5

Area = 14 cm^2

Therefore, the area of the parallelogram is 14 square centimeters.

Conclusion

The area of the parallelogram with diagonals of 8 cm and 14 cm, and an angle of 45 degrees between them, is 14 square centimeters.