The base of the trapezoid is 18 and 12 one of the lateral sides is 6 and the tg of the angle

The base of the trapezoid is 18 and 12 one of the lateral sides is 6 and the tg of the angle between it and one of the bases is √2 / 4 find the area of the trapezoid

Let’s build the height BH of the trapezoid.

Let in a right-angled triangle ABH leg BH = X cm, leg AH = Y cm.

By the Pythagorean theorem, X ^ 2 + Y ^ 2 = AB ^ 2 = 36. (1)

tgA = BH / AH = X / Y = √2 / 4 see (2).

Let’s solve the system of equations 1 and 2.

Y = 4 * X / √2.

Y ^ 2 = 8 * X ^ 2, substitute in equation 1.

X ^ 2 + 8 * X ^ 2 = 36.

X ^ 2 = 36/9 = 4.

X = BH = 2 cm.

Determine the area of the trapezoid.

Savsd = (BC + AD) * BH / 2 = (12 + 18) * 2/2 = 30 cm2.

Answer: The area of the trapezoid is 30 cm2.