The degree measure of the acute angle of a rectangular trapezoid is 45 degrees, and the height drawn
| June 15, 2021 | education
The degree measure of the acute angle of a rectangular trapezoid is 45 degrees, and the height drawn from the top of the obtuse angle divides the trapezoid into a triangle and a square whose area is 36 cm square. Calculate the area of the trapezoid.
Since ABCH is a square, and its area is 36 cm2, the length of its side is equal to the square root of the area.
AB = BC = CH = AH = √36 = 6 cm.
In a right-angled triangle CDH, one of the acute angles is 45, then the triangle is isosceles, DH = CH = 6 cm.
Determine the length of the larger base of the trapezoid.
AD = AH + DH = 6 + 6 = 12 cm.
Determine the area of the trapezoid.
Savsd = (ВС + АD) * СН / 2 = (6 + 12) * 6/2 = 54 cm2.
Answer: The area of the trapezoid is 54 cm2.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
