Answer:
Area of the trapezium ABDE = 30 cm²
Step-by-step explanation:
Area of a trapezium = [tex]\frac{1}{2}(b_1+b_2)h[/tex]
Here, [tex]b_1[/tex] and [tex]b_2[/tex] are the parallel sides of the trapezium
h = Distance between the parallel sides
From the picture attached,
ΔCAE and ΔCBD are the similar triangles.
So by the property of similarity their sides will be proportional.
[tex]\frac{AE}{BD}= \frac{CE}{CD}[/tex]
[tex]\frac{9}{6}=\frac{CE}{8}[/tex]
CE = [tex]\frac{9\times 8}{6}[/tex]
CE = 12 cm
Therefore, DE = CE - CD
DE = 12 - 8 = 4 cm
Now area of trapezium ABDE = [tex]\frac{1}{2}(AE+BD)(DE)[/tex]
= [tex]\frac{1}{2}(6+9)4[/tex]
= 30 cm²
Therefore, area of the trapezium ABDE = 30 cm²
