Answer:
Area is 33 square units.
Step-by-step explanation:
Given an isosceles trapezoid has base angles of 45° and bases of lengths 8 and 14. we have to find the area of trapezoid.
In order to find area we have to find the height.
As given trapezoid is isosceles
⇒ [tex]DE=CF=\frac{14-8}{2}=3units[/tex]
[tex]tan\theta =\frac{Perpendicular}{Base}=\frac{Height}{DE}[/tex]
[tex]tan 45 = \frac{height}{3}[/tex]
[tex]height =3 \times tan (45)[/tex]
[tex]height =3\times 1=3units[/tex]
Now, area can be calculated as
[tex]Area=\frac{1}{2}\times(\text{Sum of parallel sides}\times height[/tex]
[tex]Area =\frac{(8 + 14)}{2} \times height[/tex]
[tex]Area =\frac{22}{2}\times 3=33 units^2[/tex]
