Calculate the area of a trapezoid ABCD with bases AD and BC if AD = 27 cm, BC = 13 cm CD = 10 D = 30 degrees.

univerkov | July 2, 2021 | education

The area of the trapezoid is equal to half the sum of the bases times the height.

Let’s find the height of this trapezoid.

Let’s draw it from corner C to the base of AD.

Then we get one hundred triangle CHD – right-angled. Since the angle D = 30 °, the opposite side of CH will be equal to half of the hypotenuse CD, i.e. CH = 1/2 * CD = 1/2 * 10 = 5 cm.

Thus, we know all the necessary quantities to find the area of a trapezoid:

S = 1/2 * (27 + 13) * 5 = 1/2 * 40 * 5 = 20 * 5 = 100 cm ^ 2.

Thus, we found the area of the trapezoid.

Answer: 100 cm ^ 2.

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