1. Draw the height BE to the base AD.
2. AE: AB = cosine of angle A = 1/2.
AE = AB x 1/2 = 10 x 1/2 = 5 cm.
3. The geometric figure given in the problem statement is an isosceles trapezoid, since AB = CD.
4. According to the properties of an isosceles trapezoid, the segment AE = (AD – BC) / 2.
AD – BC = 2 x AE = 2 x 5 = 10.
AD = 10 + BC = 10 + 12 = 22 cm.
5. The total length of the sides and bases of the trapezoid (perimeter) is equal to AB + CD + BC + AD = 10 + 10 + 12 + 22 = 54 cm.
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