Question

An isosceles trapezoid has base angles of 45° and bases of lengths 8 and 14. The area of the trapezoid is

Answer 1

A = (b + b) h/2
A = (8 + 14)3/2
A = (22)3/2
A = 66/2
A = 33 units.

Answer 2

Area is 33 square units.

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

⇒
`DE=CF=(14-8)/(2)=3units`

`tan\theta =(Perpendicular)/(Base)=(Height)/(DE)`

`tan 45 = (height)/(3)`

`height =3 * tan (45)`

`height =3* 1=3units`

Now, area can be calculated as

`Area=(1)/(2)*(\text{Sum of parallel sides}* height`

`Area =((8 + 14))/(2) * height`

`Area =(22)/(2)* 3=33 units^2`