In a rectangular trapezoid ABCD, the diagonal AC is perpendicular to the side CD BC = 9
| July 5, 2021 | education
In a rectangular trapezoid ABCD, the diagonal AC is perpendicular to the side CD BC = 9 AC = 15 AD = 25 find the area of the trapezoid.
From the top of the obtuse angle of the trapezoid, we lower the height CH.
Quadrangle ABCH is a rectangle, then side AH = BC = 9 cm.
In a right-angled triangle ACH, according to the Pythagorean theorem, we determine the length of the leg CH.
CH ^ 2 = AC ^ 2 – AH ^ 2 = 15 ^ 2 – 9 ^ 2 = 225 – 81 = 144.
CH = 12 cm.
Determine the area of the trapezoid.
Savsd = (AD + BC) * CH / 2 = (25 + 9) * 12/2 = 204 cm2.
Answer: The area of the trapezoid is 204 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.
