In an isosceles trapezoid, the acute angle is 60 °, the length of the smaller base is 14 cm

In an isosceles trapezoid, the acute angle is 60 °, the length of the smaller base is 14 cm, the length of the lateral side is 10 cm. calculated the perimeter of the trapezoid.

An isosceles trapezoid is called, in which the sides are equal, and the angles at the bases are equal:

AB = СD;

∠А = ∠D;

∠В = ∠С.

Let’s draw the heights of the ВН and СK from the obtuse corners of the trapezoid. The segments AH and КD will be equal to each other, since the trapezoid is isosceles. In order for a larger base, it is necessary to calculate the length of these segments.

To do this, consider the triangle ΔАВН.

To calculate the length of the segment AH, it is most convenient to apply the cosine theorem:

cos A = AH / AB;

AH = AB · cos A;

cos 60º = 1/2;

AH = 10 1/2 = 10/2 = 5 cm.

Since the length of the larger base is equal to the sum of the segments AH, НK and KD:

AD = AН + НK + KD;

AD = 5 + 14 + 5 = 24 cm.

The perimeter of a trapezoid is the sum of the lengths of its sides:

P = AB + BC + СD + AD;

P = 10 + 14 + 10 + 24 = 58 cm.

Answer: the perimeter of the trapezoid is 58 cm.