In an isosceles trapezoid of the base 42 cm and 54 cm, the angle at the base is 45 °. Find the area of the trapezoid.

Let’s find into which segments the height of the trapezoid divides the lower base.

a = (54 cm – 42 cm) ÷ 2 = 6 cm.

The segment a, equal to 6 cm, is the leg of a right-angled triangle, the height of the trapezium is the second leg of this triangle, and the lateral side is the hypotenuse. Since the angle at the base is 45 °, then a right-angled triangle is isosceles, and the height is equal to the first leg and is equal to 6 cm.

Knowing the height of the trapezoid, we find its area.

S = (54 cm + 42 cm) ÷ 2 * 6 cm = 288 cm².

Answer: the area of the trapezoid is 288 cm².

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