Calculate the area of a trapezoid ABCD with bases AD and BC if AD = 24 cm, BC = 16 cm, ے A = 45 °, ے D = 90 °

univerkov | January 16, 2021 | education

Let’s finish the height of the HВ trapezoid.
The quadrilateral ВСDН is a rectangle, since the angle D, by condition, is equal to 900, and the ВН is the height of the trapezoid, then DН = ВС = 16 cm.
Let us determine the length of the segment AH. AH = AD – DН = 24 – 16 = 8 cm.
In a right-angled triangle ABН, one of the acute angles is 450, then the legs of this triangle are equal in length. AH = BH = 8 cm.
Determine the area of the trapezoid.
Savsd = (ВС + AD) * ВН / 2 = (16 + 24) * 8/2 = 160 cm2.
Answer: The area of the trapezoid is 160 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.