In a rectangular trapezoid ABCD, the lateral side AB = 10cm. Bigger base AD = 18cm, angle D

univerkov | September 25, 2021 | education

In a rectangular trapezoid ABCD, the lateral side AB = 10cm. Bigger base AD = 18cm, angle D = 45. Find the area of the trapezoid.

Let us draw the height CH from the top of the obtuse angle C. Since the trapezoid is rectangular, and CH is the height of the trapezoid, the quadrilateral ABCH is a rectangle. Then CH = AB = 10 cm.

Triangle СDH is rectangular, in which the angle DCH = 180 – СHD – СDH = 180 – 90 – 45 = 450.

Then the triangle CDH is rectangular and isosceles, DH = CH = 10 cm.

The length of the segment AH = AD – DH = 18 – 10 = 8 cm, then BC = AH = 8 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (8 + 18) * 10/2 = 130 cm2.

Answer: The area of the trapezoid is 130 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.