Math problem

Question

ABCD is a trapezoid, m∠B= 90º, m∠ACD = 90º, AB = BC, AC = CD, AD = 12. Find: Area of ABCD.

Answer 1

draw the trapezoid

triangle ACD is a right isosceles triangle

AD^2=AC^2+CD^2 and AC=CD

12^2=2*AC^2

144=2*AC^2

72=AC^2

AC=√72

triangle ABC is a right isosceles triangle

AC^2=AB^2+BC^2 and AB=BC

(√72)^2=2*AB^2

72=2*AB^2

36=AB^2

AB=6

BC=6

AD is one base and BC is the other base while AB is the height

A=(1/2)(h)(B+b)

A=(1/2)(6)(12+6)

A=(1/2)(6)(18)

A=3*18

A=54 square units