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As ΔABC is similar to ΔDEC, BEC is a straight line and AB//DE.

Since AB:DE = 2:1, 

area of ΔABC : area of ΔDEC = 4:1

In ΔDEC, DF : FC = 3:4, so

area of ΔDFE : area ofΔFCE= 3:4

Since ΔDEC = ΔDFE + ΔFCE

If area of ΔDEC = 1, area of ΔDFE = 3/7

Therefore, area of ΔABC : area of ΔDFE = 4 : 3/7 = 4X7 : 3 = 28 :3

 

 

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Why is area of ΔABC : area of ΔDEC = 4:1?

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Triangle area equals to height x base/2. Similar triangles will share same ratio for all sides and height. I.e. AB:DE=2:1 hence, BC:EC = AC:DC. Therefore, the triangle area ratio = 2×2 : 1×1 = 4:1.

Hope this explains.

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