Calculate the area of a trapezoid ABCD with bases AD and BC if AD = 24 cm, BC = 16 cm, angle A = 45

univerkov | August 8, 2021 | education

Calculate the area of a trapezoid ABCD with bases AD and BC if AD = 24 cm, BC = 16 cm, angle A = 45 degrees, angle D = 90 degrees.

1. From the angle B of the trapezoid ABCD, we lower the height BO to the base AD, which forms the right-angled triangle ABO. In this triangle, the angle is A = 45 °, O = 90 °, B = 180 – (90 + 45) = 45 °. Side AO = 24 – 16 = 8 centimeters, and therefore a height of 8 centimeters, since the side AO = BO (lie opposite equal angles).

2. Let’s calculate what is the value of the area of the trapezoid.

(16 + 24) / 2 * 8 = 160 cm².

Answer: 160 square centimeters.

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