Answer:
Option A is correct.
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 isosceles trapezoid.
An isosceles trapezoid has base angles of 45° and bases of lengths 8 and 14.
From the figure attached , we can see an isosceles trapezoid ABCD,
AB = 8cm and CD=14cm
So we have to find the value of AE which is the height of Trapezoid in order to find area.
In ΔAED
\(tan\angle 45 =\frac{AE}{ED}\)
⇒ \(AE=1\times 3\)
∴ AE = DE =3cm
\(\text{The area of the trapezoid=}\frac{h}{2}\times (a+b)\)
h=3cm, a=14cm, b=8cm
\(Area=\frac{3}{2}\times(14+8)=\frac{3}{2}\times 22=33 units^2\)
hence, \(\text{The area of the trapezoid is }33 units^2\)
Option A is correct.
