Question

Дано:ABCD-параллелограмм,AB-8,1см,диагональ-14см,угол между стороной AB и диагональю-30градусов.Найти:площадь ABCD

Answer 1

Решение: Sabcd=a*b*sin альфа Sabc=1÷2a*b*sin альфа Sabc=1/2*14*8.1*1/2=28,35cм^2 Т.К Sabc=Sadc (по 2 сторонам и углу)то Sabcd=2 abc Sabcd=2*28.35см^2=56.7см^2 ответ:56.7см^2

Answer 2

Given information:

- ABCD is a parallelogram. - AB = 8.1 cm. - Diagonal = 14 cm. - Angle between side AB and the diagonal = 30 degrees.

Approach to find the area of ABCD:

To find the area of ABCD, we need to know the height (perpendicular distance) from side AB to side CD. Since the given angle is between side AB and the diagonal, we can use trigonometry to find the height.

Let's find the height using the given information.

Finding the height:

The height can be found using the formula: height = Diagonal * sin(angle)

Substituting the given values: height = 14 cm * sin(30 degrees)

Calculating the height:

height = 14 cm * 0.5 height = 7 cm

Finding the area:

The area of a parallelogram is given by the formula: Area = base * height

In this case, the base is AB, which is given as 8.1 cm, and the height is 7 cm (calculated above).

Calculating the area:

Area = 8.1 cm * 7 cm Area = 56.7 cm^2

Hence, the area of parallelogram ABCD is 56.7 square centimeters.