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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