Firstly, we will draw figure
now, we will draw a altitude from B to DC that divides trapezium into rectangle and right triangle
because of opposite sides of rectangle ABMD are congruent
so,
DM=AB=9
CM=CD-DM
CM=18-9
CM=9
now, we can find BM by using Pythagoras theorem
[tex] BM=\sqrt{BC^2-CM^2} [/tex]
now, we can plug values
we get
[tex] BM=\sqrt{15^2-9^2} [/tex]
[tex] BM=12 [/tex]
now, we can find area of trapezium
[tex] A=\frac{1}{2} (AB+CD)*(BM) [/tex]
now, we can plug values
and we get
[tex] A=\frac{1}{2} (9+18)*(12) [/tex]
[tex] A=162cm^2 [/tex]
so, area of of the trapezoid is [tex] 162cm^2 [/tex]..........Answer
