Find the area of a rectangular trapezoid, the bases of which are 4 and 6 cm, and one of the angles is 135 degrees.

| September 2, 2021 | education

A rectangular trapezoid is called, in which one of the lateral sides is height, so its two corners are straight.

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

S = (BC + AD) / 2 h.

Suppose AB is the large side, BH is the height, and the angle B is 135 °.

Consider the triangle ABH. The segment AH is equal to the difference in the length of the bases:

AH = AD – BC;

AH = 6 – 4 = 2 cm.

Since the sum of the degree measures of the angles adjacent to one side is 180 °, the angle A is equal to:

∠А = 180 ° – 135 ° = 45 °.

We can find the BH height by applying the tangent of the angle a:

tg A = BH / AH;

tg 45 ° = 1;

BH = AH · tg A;

BH = 2 1 = 2 cm.

S = (4 + 6) / 2 2 = 10 cm2.

Answer: the area of ​​the trapezoid is 10 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.