In a rectangular trapezoid ABCD with base AD and BC, angle A = angle B = 90 degrees, angle ACD

| September 17, 2021 | education

In a rectangular trapezoid ABCD with base AD and BC, angle A = angle B = 90 degrees, angle ACD = 90 degrees BC = 4 cm. AD = 16 cm.

Let’s draw the CH height from the top of the obtuse angle. The formed quadrangle ABCH is rectangular, since AB is perpendicular to BC and AD and CH is perpendicular to BC and AD, then AH = BC = 4 cm.

Then the length of the segment DН = АD – АН = 16 – 4 = 12 cm.

The ACD triangle is rectangular by condition, the CH height is drawn to the hypotenuse from a right angle. Then the length of the height is equal to the square root of the product of the lengths of the segments by which the height divides the hypotenuse.

CH = √ (AN * DH) = √ (4 * 12) = √48 = 4 * √3 cm.

Determine the area of ​​the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (4 + 16) * 4 * √3 / 2 = 40 * √3 cm2.

Answer: The area of ​​the trapezoid is 40 * √3 cm2.



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