The larger base and large side of the rectangular trapezoid are a (alpha) cm,

| August 11, 2021 | education

The larger base and large side of the rectangular trapezoid are a (alpha) cm, and one of the corners is 60 degrees. Draw the area of the trapezoid.

Since, by condition, CD = AD = a cm, then the ACD triangle is isosceles, and since it has one of the angles equal to 60, then ACD is an equilateral triangle.

Let’s draw the height of CH, which in an equilateral triangle is both the bisector and the median, then AH = DH = AD / 2 = a / 2 cm.

The length of the height in an equilateral triangle is: CH = a * √3 / 2 cm.

Since the trapezoid is rectangular, and CH is the height, then the quadrangle ABCH is a rectangle, and then BC = AH = a / 2 cm.

Determine the area of ​​the trapezoid.

Sassd = (BC + AD) * H / 2 = ((a / 2 + a) * a * √3 / 2) / 2 = 3 * a * √3 / 8 cm2.

Answer: The area of ​​the trapezoid is 3 * a * √3 / 8 cm2.



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