Answer:
The area of Trapezium is 171 cm² .
Step-by-step explanation:
Given as for a trapezium :
The measure of parallel sides are 25 cm and 13 cm
I.e AB = 25 cm , CD = 13 cm
The measure of other sides of the trapezium = AD = BC = 15 cm
Let The height of measure h is drawn on the side AB
So , The BOC is now a triangle
∴ The measure of BO = AB - AO = 25 cm - 13 cm = 12 cm
Let the area of Trapezium = A
Now, height h = [tex]\sqrt{BC^{2} - OB^{2} }[/tex]
Or, h = [tex]\sqrt{15^{2} - 12^{2} }[/tex]
Or, h = [tex]\sqrt{225 - 144 }[/tex]
∴ h = [tex]\sqrt{81}[/tex]
I.e h = 9 cm
From figure
∵ Area of trapezium = [tex]\frac{1}{2}[/tex]×Height×( sum of parallel side )
or, A = [tex]\frac{1}{2}[/tex]×h×( AB + CD )
or , A = [tex]\frac{1}{2}[/tex]×9×( 25 + 13 )
Or, A = [tex]\frac{1}{2}[/tex]×9×38
∴ Area = 171 cm²
Hence The area of Trapezium is 171 cm² . Answer
