In an isosceles trapezoid, the larger base is 40 cm, the lateral side is 18 cm, and the angle

| September 24, 2021 | education

In an isosceles trapezoid, the larger base is 40 cm, the lateral side is 18 cm, and the angle between them is 60 °. Find the perimeter of the trapezoid.

To calculate the perimeter of a trapezoid, you need to calculate the length of all its sides.

Since the length of the smaller base is equal to the length of the part of the larger base, which is located between two heights, then:

ВС = НК = АD – АН – КD.

Since the trapezoid is isosceles, the segments AH and KD are equal. To calculate their length, consider the triangle ΔАВН.

To calculate the length BH, we apply the cosine theorem, according to which the cosine of an acute angle in a right triangle is the ratio of the adjacent leg to the hypotenuse:

cos A = AH / AB;

AH = AB · cos A;

cos 60 ° = 1/2;

AH = 18 1/2 = 9 cm.

BC = HK = 40 – 9 – 9 = 22 cm.

P = AB + BC + CD + AD;

P = 22 + 18 + 40 + 18 = 98 cm.

Answer: the perimeter of the trapezoid is 98 cm.



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