An isosceles trapezoid has bases of 4 and 10. if the base angle is 45°, find the area.

a: 42 sq. units
b: 21√2 sq. units
c: 21 sq. units

Draw this trapezoid, let it be ABCD, where AB is the smaller base (=4) and
DC, the larger one (=10)
From A & B draw the altitude AA' & BB'. You notice that ABA'B' is a rectangle and A'B' = 4,. You conclude that DA' = B'C = 3 .
Now let's calculate the altitude AA'.
The right triangle ADA' is also an isosceles right triangle:
( angle DA'A=90, angle ADA' = 45 and angle DAA' =45) , then
DA' = AA' (altitude) = 3 units. Now we can calculate the area of the trapezoid:  
 Area = (B+b).H/2

Area = (4+10)x3/2 = 14x3/2 = 42/2 = 21 sq.unit