The large side of the rectangular trapezoid = 50 cm, and the smaller base is 20 cm, the diagonal of the trapezoid

| August 12, 2021 | education

The large side of the rectangular trapezoid = 50 cm, and the smaller base is 20 cm, the diagonal of the trapezoid divides its obtuse angle in half. find the area of the trapezoid

Since the diagonal AC is the bisector of the angle BCD, the angle ACB = ACD. Angle CAD = ACB as criss-crossing angles at the intersection of parallel straight lines BC and AD secant AC, then angle ACD = CAD, and triangle ACD is isosceles, AD = CD = 50 cm.Let us draw the height of CH, which forms rectangle ABCN, then AH = BC = 20 cm, and DH = AD – AH = 50 – 20 = 30 cm.

From the right-angled triangle CHD, we determine the length of the CH height.

CH ^ 2 = CD ^ 2 – DH ^ 2 = 2500 – 900 = 1600.

CH = 40 cm.

Determine the area of the trapezoid. Savsd = (ВС + АD) * СН / 2 = 70 * 40/2 = 2800/2 = 1400 cm2.

Answer: The area of the trapezoid is 1400 cm2.



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