Question

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Answer 1

Answer:

30 cm^2

Solution,

$\frac{BD}{CD} = \frac{AE}{CE} \\ or \: \frac{6}{8} = \frac{9}{8 + DE} \\ or \: 48 + 6(DE) = 72 \\ or \: 6(DE) = 72 - 48 \\ or \: 6(DE) = 24 \\ or \: DE= \frac{24}{6} \\ DE = 4 \\ ce = 8 + 4 = 12 \\ area \: of \: trapezoid \\ = area \: \: of \: aec - area \: of \:bdc \\ = \frac{1}{2} (a)(12) - \frac{1}{2} (6)(8) \\ = 54 - 24 \\ = 30 \: {cm}^{2}$

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Answer 2

Answer:

Area = 30 cm²

Step-by-step explanation:

Finding DE first:

ΔCDB is similar to ΔCEA

So, To find DE, We'll take the proportion of their sides:

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

Cross Multiplying

=> 6CE = 72

Dividing both sides by 6

=> CE = 12 cm

Now

DE = CE - CD

DE = 12-8

DE = 4 cm

Now, Finding the Area of trapezium:

=> Area = $\frac{a+b}{2} (Height)$

Where a = 6, b = 9 and Height = 4

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

=> Area = 2(15)

=> Area = 30 cm²