The bases of an isosceles trapezoid are 9 cm and 21 cm, and its acute angle is 60 °. Find the perimeter of the trapezoid.

| April 25, 2021 | education

Let us lower the height from the top of the obtuse angle C to the larger base AD.

By the property of an isosceles trapezoid, the height lowered from the apex of an obtuse angle to the larger base divides it into two segments, the smaller of which is equal to the half-difference of the bases, and the larger half-sum of the bases.

DН = (АD – ВС) / 2 = (21 – 9) / 2 = 12/2 = 6 cm.

In a right-angled triangle СНD, we define the value of the angle НСD.

Angle НСD = 180 – 90 – 60 = 30.

The HD leg lies opposite an angle of 30, therefore, it is equal to half the length of the CD hypotenuse.

Then СD = НD * 2 = 6 * 2 = 12 cm.

Since the trapezoid is isosceles, then AB = CD = 12 cm.

Determine the perimeter of the trapezoid.

P = AB + BC + CD + AD = 12 + 9 + 12 + 21 = 54 cm.

Answer: The perimeter of the trapezoid is 54 cm.



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