In the Trapezium, one of the lateral sides is perpendicular to the base, angle = 110gr

univerkov | January 8, 2021 | education

In the Trapezium, one of the lateral sides is perpendicular to the base, angle = 110gr, and the base is 8 cm and 10 cm. Find the area of the trapezoid.

Let’s build the height of the CH. Since the trapezoid is rectangular, and CH is height, then the quadrilateral ABCH is a rectangle, then AH = BC = 8 cm.
The length of the segment DH = AD – AH = 10 – 8 = 2 cm.
The sum of the angles of the trapezoid at the lateral side is 180, then the angle CDH = (180 – 110) = 70. In a right-angled triangle CDH tg70 = CH / DH.
CH = DN * tg70 = 2 * tg70 cm.
Determine the area of the trapezoid.
Savsd = (DC + AD) * CH / 2 = (8 + 10) * 2 * tg70 / 2 = 18 * tg700 cm2.
Answer: The area of the trapezoid is 18 * tg700 cm2.

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