An isosceles trapezoid has base angles equal to 45 and bases of lengths 6 and 12. find the area of the trapezoid.

Area of isosceles trapezoid(A) is given by:

where

a and b are the unequal side length and

h is the height of the isosceles trapezoid.

Given that:

An isosceles trapezoid has base angles equal to 45 and bases of lengths 6 and 12.

See the diagram as shown below.

In isosceles trapezoid ABCD

AB = 6 units , CD = 12 units

AB = EF = 6 units

In triangle AED:

Since, DE=FC = 3 units

We need to find the value of AE:

Use tangent ratio in triangle AED:

Then;

Substitute the given values we have;

⇒ units

In the given isosceles ABCD:

AE = height = 3 units

AB = 6 units and CD = 12 units

then using area formula:

Substitute the given values we have;

sqaure units.

Therefore, the area of the isosceles trapezoid is, 27 square units

c

step-by-step explanation: easy math