Calculate the area of a trapezoid ABCD with base AD and BC if AD = 27cm BC = 13cm, CD = 10cm

| August 18, 2021 | education

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

The area of the trapezoid is determined by the formula:

S = (a + b) / 2 * h (a and b are the bases of the trapezoid, h is the height).

From the condition of the problem => a = 27, b = 13, and the height is unknown. Let’s take advantage of the fact that the leg of a right-angled triangle, lying opposite an angle of 30 degrees, is equal to half of the hypotenuse.

The height of the trapezoid, pubescent from the top of the C, forms a rectangle with a hypotenuse of 10 cm and lies opposite an angle of 30 °, therefore h = 5.

Since all the necessary components are available;

S = (a + b) / 2 * h = (27 + 13) / 2 * 5 = 25.

Answer: 25 (sq. Units).



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