In a rectangular trapezoid, the smaller base is 3 cm, the larger side is 4 cm, and one of the corners

In a rectangular trapezoid, the smaller base is 3 cm, the larger side is 4 cm, and one of the corners of the trapezoid is 150 degrees.

A trapezoid is a quadrangle, two opposite sides of which are parallel to each other, and the other two are not parallel.

Parallel sides of a trapezoid are called bases, and non-parallel sides are called sides.

The area of ​​the trapezoid is calculated using the formula:

S = (a + b) / 2 h; Where:

S is the area of ​​the trapezoid;

a – smaller base;

b – larger base;

h – height.

In order to calculate the area, you need to find the length of the larger base and the height of the trapezoid. To do this, consider the triangle ΔАВН.

The НВС angle is right, as it is created with the help of the HV perpendicular. Based on this:

∠АВН = 150 ° – 90 ° = 60 °.

Using the sine theorem, we calculate the length of the VN height.

The sine of an acute angle of a right-angled triangle is the ratio of the adjacent leg to the hypotenuse:

sin B = BH / AB;

BH = AB · sin B;

sin 60 ° = 1/2;

BH = 4 1/2 = 2 cm.

Now, behind the Pythagorean theorem, we find the segment AN:

AB ^ 2 = BH ^ 2 + AH ^ 2;

AH ^ 2 = AB ^ 2 – BH ^ 2;

AH ^ 2 = 42 – 22 = 16 – 4 = 12;

AH = √12 ≈ 3.46.

Since the length of the segment located between the perpendiculars is equal to the length of the smaller base, then BC = HD. Therefore:

AD = AH + HD;

AD = 3 + 3.46 = 6.46;

S = (3 + 6.46) / 2 2 = 9.46 cm2.

Answer: the area of ​​the trapezoid is 9.46 cm2.