In the trapezoid abcd, the angle is a = b = 90 degrees, ab = 8cm Bc = 4 cm Cd = 10 cm

univerkov | April 22, 2021 | education

In the trapezoid abcd, the angle is a = b = 90 degrees, ab = 8cm Bc = 4 cm Cd = 10 cm Find a) the area of the triangle acd; b) the area of the trapezoid abcd

Let us lower the height from the vertex C of the trapezoid ABCD.

Since, by condition, angles A and B are straight, AB is parallel and equal to CH, CH = AB = 8 cm.

Consider a right-angled triangle CHD, whose angle H is straight, the hypotenuse CD = 10 cm, and the leg CH = 8 cm. Then, by the Pythagorean theorem, we find the leg HD.

НD ^ 2 = СD ^ 2 – CH ^ 2 = 100 – 64 = 36.

НD = 6 cm.

The base of the trapezoid AD = AH + HD = 4 + 6 = 10 cm.

Then the area of the triangle СНD is equal to:

Sсhд = (СН * АD) / 2 = 8 * 10/2 = 40 cm2.

Since the quadrilateral ABCH is rectangles, then BC = AN.

Then the area of the trapezoid is:

Savsd = (ВС + АD) * СН / 2 = (4 + 10) * 8/2 = 56 cm2.

Answer:

Sasd = 40 cm2.

Savsd = 56 cm2.

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