Find the sides and area of a rectangular trapezoid if its height drawn from the top of the trapezoid is to divide the larger

| September 16, 2021 | education

Find the sides and area of a rectangular trapezoid if its height drawn from the top of the trapezoid is to divide the larger base into segments equal to 1m and 4m and one of the angles is 45 degrees

Let the CH height divide the larger base into segments AH = 1 m, DH = 4 cm.

The СDН triangle is rectangular, since СН is the height at which the СDН angle, according to the condition, is 45, then the angle DСН = 90 – 45 = 45, which means that the СDН triangle is rectangular and isosceles.

Then CH = DH = 4 m.By the Pythagorean theorem, CD ^ 2 = CH ^ 2 + DH ^ 2 = 16 + 16 = 32.

СD = 4 * √2 cm.

Quadrangle ABCN is a rectangle, then BC = AH = 1 m, AB = CH = 4 m. AD = AH + DH = 1 + 4 = 5 cm.

Determine the area of the trapezoid. Str = (BC + AD) * CH / 2 = (1 + 5) * 4/2 = 12 cm2.

Answer: The area of the trapezoid is 12 cm2, the sides are 4 cm, 1 cm, 4 * √2 cm, 5 cm.



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