Question

Work out the area of the trapezium ABDE

Answer 1

Answer:

Area of trapezium ABCD is 30 cm²

Step-by-step explanation:

Since area of trapezium = $\frac{1}{2}$ ( sum of bases ) × distance

between the bases

= $\frac{1}{2}$ [ BD + AE ] × DE

We know BD = 6 cm

               AE  =  9 cm

  and       DE = ( CE - CD )

In two similar triangle BCD and ACE

$\frac{CE}{CD}$ = $\frac{AE}{BD}$

CE = $\frac{CD\times AE}{BD}$

     = $\frac{8\times 9}{6}$

     = 12 cm

Now DE = CE - CD

             = 12 - 8 = 4 cm

Area of trapezium = $\frac{1}{2}$ ( 6 + 9 ) × 4

                             = 2 × 15

                             = 30 cm²

Answer 2

The two triangles seen in the picture are simular (congruent) and one is enlarged.

scale factor= 9÷6 = 1.5

8×1.5 =12 (the side length of the triangle)

12-8=4 (bottom side length of trapezium)

area of trapezium= 1/2× ((a+b)×h)

1/2×((6+9)×4)=24cm^2