The large side of the rectangular trapezoid is 28 cm, and the acute angle is 30 degrees.
January 14, 2021 | education
| The large side of the rectangular trapezoid is 28 cm, and the acute angle is 30 degrees. Find the area of the trapezoid if a circle can be inscribed into it.
Let’s draw the CH height from the top of the obtuse angle. In a right-angled triangle, the CH leg, the CH leg lies opposite the angle of 30, which means that its length is equal to half the length of the СD hypotenuse. CH = СD / 2 = 28/2 = 14 cm.Then AB = CH = 14 cm.
The sum of the lengths of the lateral sides of the trapezoid is: AB + СD = 14 + 28 = 42 cm.
Since a circle can be inscribed into the trapezoid, AB + СD = BC + AD = 42 cm.
Determine the area of the trapezoid. Savsd = (ВС + AD) * CH / 2 = 42 * 14/2 = 294 cm2.
Answer: The area of the trapezoid is 294 cm2.
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