Answer:
[tex]\boxed{\bold{\huge{\boxed{Area\ of\ Trapezium = 150\ cm\²}}}}[/tex]
Step-by-step explanation:
Using Pythagorean Theorem first to find EC
[tex]\sf CB^2 = EB^2+EC^2\\Where \ CB = 13 \ and \ EB = 5 \\13^2 = 5^2 + EC^2 \\169 - 25 = EC^2 \\EC^2 = 144\\Taking \ sqrt \ on \ both \ sides\\EC = 12 \ cm[/tex]
Given that:
AE = EC
AE = 12 cm
Now,
AB = AE + EB
AB = 12 + 5
AB = 17 cm
ABCD is a trapezoid / trapezium
So,
Area of Trapezium = [tex]\sf \frac{AB+DC}{2} (EC)[/tex]
Where AB = 17 , DC = 8 and EC = 12
Area of Trapezium = [tex]\sf \frac{17+8}{2} ( 12)[/tex]
Area of Trapezium = (25)(6)
Area of Trapezium = 150 cm²
