Question

Work out the area of the trapezium ABDE. B 9 cm 6 cm 8 cm →D E

Answer 1

Answer:

Area of the trapezium ABDE = 30 cm²

Step-by-step explanation:

Area of a trapezium = $\frac{1}{2}(b_1+b_2)h$

Here, $b_1$ and $b_2$ 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.

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

$\frac{9}{6}=\frac{CE}{8}$

CE = $\frac{9\times 8}{6}$

CE = 12 cm

Therefore, DE = CE - CD

DE = 12 - 8 = 4 cm

Now area of trapezium ABDE = $\frac{1}{2}(AE+BD)(DE)$

                                                  = $\frac{1}{2}(6+9)4$

                                                  = 30 cm²

Therefore, area of the trapezium ABDE = 30 cm²