In trapezoid ABCD, angle A = 60 degrees, angle D = 45 degrees, sides 10 and 12 cm

univerkov | June 26, 2021 | education

In trapezoid ABCD, angle A = 60 degrees, angle D = 45 degrees, sides 10 and 12 cm, and the smaller base 8 cm. Find the midline of the trapezoid

Let’s draw the heights of the ВН and СK.

Then, in a right-angled triangle ABН, the leg AH = AB * CosBAH = 10 * 1/2 = 5 cm.

In a right-angled triangle CDK, the leg DK = CD * CosCDK = 12 * √2 / 2 = 6 * √2.

Base length АD = АН + НК + DК = 5 + 8 + 6 * √2 = 13 + 6 * √2 cm.

Let’s define the middle line of the trapezoid.

МР = (ВС + АD) / 2 = (8 + 13 + 6 * √2) / 2 = (21 + 6 * √2) / 2 = 10.5 + 3 * √2 cm.

Answer: The middle line of the trapezoid is 10.5 + 3 * √2 cm.

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