In the trapezoid ABCD AD and BC are the bases, the angle A = 90 * (degrees), BC = 4 cm
| July 22, 2021 | education
In the trapezoid ABCD AD and BC are the bases, the angle A = 90 * (degrees), BC = 4 cm, CD = 10 cm. The height of CK is 8 cm. Find the area of the trapezoid.
From the right-angled triangle CDK, by the Pythagorean theorem, we determine the length of the leg DK.
DK ^ 2 = CD ^ 2 – CK ^ 2 = 10 ^ 2 – 8 ^ 2 = 100 – 64 = 36.
DK = 6 cm.
Quadrangle ABCK is a rectangle, since BC is parallel to AD, and AK belongs to AD, the angle A is 90 by condition, and SK is the height of the trapezoid, then AK = BC = 4 cm.
Let’s determine the length of the base AD.
AD = AK + DK = 4 + 6 = 10 cm.
Determine the area of the trapezoid.
S = (BC + AD) * CK / 2 = (4 + 10) * 8/2 = 56 cm2.
Answer: The area of the trapezoid is 56 cm2.
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