The bases of the trapezoid are 18 and 12, one of the sides is 6, the tangent of the angle between it and one of the bases
| January 16, 2021 | education
The bases of the trapezoid are 18 and 12, one of the sides is 6, the tangent of the angle between it and one of the bases is equal to the root of 2/4. find the area of the trapezoid
Consider a right-angled triangle ABE, which has a leg BE and a trapezoid height, and tgA = √2 / 4.
TgA = BE / AE = √2 / 4.
AE = 4 * BE / √2 = 2 * BE * √2.
By the Pythagorean theorem, AE^2 = AB^2 – BE^2 = 36 – BE^2.
(2 * BE * √2) 2 = 36 – BE^2.
8 * BE^2 = 36 – BE^2.
9 * BE^2 = 36.
BE^2 = 4.
BE = 2 cm.
Find the area of the trapezoid.
S = (BC + AD) * BE / 2 = (12 + 18) * 2/2 = 30 cm2.
Answer: S = 30 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.
