1. The area of the trapezoid is equal to the product of the half-sum of its bases by the height.
2. Find the height h.
To do this, from the vertex B we lower the perpendicular DO to the base of the trapezoid AD – we get a right-angled triangle ABO, in which, according to the condition of the problem, the angle A is 45 *, leg AO = (AD – BC): 2 = (20 – 10): 2 = 5.
The leg BО, which is the height of the trapezoid, is calculated by the tangent 45 *.
h: AO = tg 45 * = 1;
h = AO * 1 = 5.
3. Let’s calculate what is the area S of the trapezoid.
S = (BC + AD) * h: 2 = (10 + 20) * 5: 2 = 75.
Answer: The area of a trapezoid is 75 square units.
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