The lesser base of an isosceles trapezoid is 4, and the lateral side is 6 and the angle between

| February 15, 2021 | education

The lesser base of an isosceles trapezoid is 4, and the lateral side is 6 and the angle between these sides is 120 °. Find the area of this trapezoid.

Let’s build the heights of the HВ and CM trapezoid.

The quadrilateral BCMН is a rectangle, then НM = BC = 4 cm, and the triangles AВН and СDM are rectangular.

In a right-angled triangle ABН, the angle ABН = ABC – СВН = 120 – 90 = 300.

Then the leg AH lies opposite an angle of 300. AH = AB / 2 = 6/2 = 3 cm.

By the Pythagorean theorem, BH^2 = AB^2 – AH^2 = 36 – 9 = 27.

BH = √27 = 3 * √3 cm.

Rectangular triangles ABН and СDM are equal in hypotenuse and acute yy, then DM = AH = 3 cm. AD = 3 + 4 + 3 = 10 cm.

Determine the area of the trapezoid.

S = (ВС + AD) * ВН / 2 = (4 + 10) * 3 * √3 / 2 = 21 * √3 cm2.

Answer: The area of the trapezoid is 21 * √3 cm2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.