Find the area of a trapezoid ABCD with base AB and CD if the angle D is 30 degrees, AB is 2 cm, CD is 10 cm, DA is 8 cm.

Let’s build the height АН to the base СD.

In a right-angled triangle ADH, the angle ADH, by condition, is equal to 30, then the leg AH lies opposite the angle 30, and therefore its length is equal to half of the hypotenuse AD.

AH = AD / 2 = 8/2 = 4 cm.

Determine the area of the trapezoid ABCD.

Savsd = (AB + CD) * AH / 2 = (2 + 10) * 4/2 = 24 cm2.

Answer: The area of the trapezoid is 24 cm2.

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