The base of the trapezoid is 8 cm and 10 cm the side of the trapezoid

The base of the trapezoid is 8 cm and 10 cm the side of the trapezoid is 6 cm, and one of the adjacent corners is 30 degrees, find the area of the trapezoid.

A trapezoid is a quadrilateral in which one pair of opposite sides is parallel, and the sides are not equal to each other.

The area of ​​a trapezoid is the product of the half-sum of its bases by the height:

S = (a + b) / 2 h, where:

S is the area of ​​the trapezoid;

a – smaller base of the BC;

b – larger base of AD;

h is the height of the trapezoid BH.

In order to calculate the area of ​​the trapezoid, we find the height BH. To do this, consider the triangle ΔАВН. This triangle is rectangular. Let’s apply the sine theorem. The sine of an acute angle of a right triangle is the ratio of the opposite leg to the hypotenuse:

sin A = BH / AB;

BH = AB ∙ sin A;

sin 30º = 1/2;

BH = 6 1/2 = 6/2 = 3 cm;

S = (8 + 10) / 2 ∙ 3 ​​= 18/2 ∙ 3 ​​= 9 ∙ 3 = 27 cm2.

Answer: the area of ​​the trapezoid is 27 cm2.