ABCDE is a pentag

Given: ABCDE is a pentagon of which side BC is parallel to diagonal AD, EP is perpendicular on BC and EP intersects AD at the point Q. BC = 7 cm, AD = 13 cm, PE = 9 cm

Also,

and PQ + EQ = PE

⇒ 4 + EQ = 9

⇒ EQ = 5 cm

Now,

Area of pentagon ABCDE = area(ΔAED) + area(trapezium ABCD)

Now, we know

Area of trapezium sum of parallel sides × Height

⇒ area(trapezium ABCD)

Also,

Area of triangle

⇒ area(ABCDE) = 40 + 32.5 = 72.5 cm²