# In an isosceles trapezoid, the side b is equal to the smaller base, and the angle

In an isosceles trapezoid, the side b is equal to the smaller base, and the angle adjacent to the larger base is alpha. Find the area of the trapezoid.

In a right-angled triangle ABH, we define the length of the legs through the angle and the hypotenuse.

Sinα = BH / b.

BH = b * Sinα.

Cosα = AH / b.

AH = b * Cosα.

Let’s draw the height DH. Since the trapezoid is isosceles, the height BH and SK cut off equal segments DK = AH = b * Cosα on a larger base.

Base length AD = AH + HK + DK = b * Cosα + b + b * Cosα = b * (1 + 2 * Cosα).

Determine the area of the trapezoid.

Savsd = (ВС + АD) * ВH / 2 = (b + b * (1 + 2 * Cosα)) * b * Sinα / 2 = (b ^ 2 * (1 + 1 + 2 * Cosα) * SInα) / 2 = (2 * b ^ 2 * (1 + Cosα) * Sinα / 2 = b2 * Sinα * (1 + Cosα) cm2.

Answer: The area of the trapezoid is: b2 * Sinα * (1 + Cosα) cm2.

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