The large lateral side of the rectangular trapezoid is 50 cm and the smaller base 20 cm deagonal

| January 14, 2021 | education

The large lateral side of the rectangular trapezoid is 50 cm and the smaller base 20 cm deagonal divides its obtuse angle in half to find the area.

If the diagonal AC divides the angle in half, then it is the bisector of the angle, and therefore cuts off the isosceles triangle of the ACD from the trapezoid, in which DA = DС = 50 cm.
Let’s draw from the top С the height СН. Since the trapezoid is rectangular, and CH is height, then the quadrangle ABСН is rectangular, which means that BC = AH = 20 cm, then DН = AD – AH = 50 – 20 = 30 cm.
From the right-angled triangle SDН, we determine the height of the trapezoid CH.
CH ^ 2 = СD ^ 2 – DН ^ 2 = 2500 – 900 = 1600.
CH = 40 cm.
Then Savsd = (ВС + AD) * CH / 2 = 70 * 40/2 = 1400 cm2.
Answer: The area of the trapezoid is 1400 cm2.



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