ABCD – isosceles trapezoid, AB = 10, angle D = 60 degrees. The bisector AC is drawn in the trapezium.

| March 16, 2021 | education

ABCD – isosceles trapezoid, AB = 10, angle D = 60 degrees. The bisector AC is drawn in the trapezium. Find the perimeter of the trapezoid.

Since, by condition, the trapezoid is isosceles, then its angles at the base are equal.

Angle BAD = ADC = 60, lateral side of CD = AB = 10 cm.

Consider a triangle ACD, in which angle D = 60, angle CAD = BAD / 2 = 30, then angle ACD = 180 – 60 – 30 = 90. Triangle ACD is rectangular, and its leg CD lies opposite angle 30, and therefore is equal to half of AD …

Then AD = 2 * CD = 2 * 10 = 20 cm.

In the ABC triangle, the BCA angle is equal to the CAD angle as criss-crossing angles at the intersection of parallel BC and AD secant AC, then the BCA angle = CAD = BAC = 30, and the ABC triangle is isosceles, since the angles at the base of the AC are equal.

Then AB = BC = 10 cm.

Determine the perimeter of the trapezoid. P = AB + BC + CD + AD = 10 + 10 + 10 + 20 = 50 cm.

Answer: The perimeter of the trapezoid is 50 cm.



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