Area of quadrilateral ACDE is 279 cm, B is the mid-point of AC, Find the area of ABE if AC||DE and BE||DC
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Area of quadrilateral ACDE is 279 cm, B is the mid-point of AC, Find the area of ABE if AC||DE and BE||DC
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[tex]\huge{\underline{\mathtt{\red{❥A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}[/tex]Given: A quadrilateral ABCD and BD is a diagonal.
To prove: ABCD is a parallelogram.
Construction: Draw AM ⊥ DC and CL ⊥ AB (extend DC and AB). Join AC, the other diagonal of ABCD.
Proof: ar(quad. ABCD) = ar(∆ABD) + ar(∆DCB)
= 2 ar(∆ABD) [∵ ar(∆ABD) = ar(∆DCB)]
∴ ar(∆ABD) = 12
ar(quad. ABCD) ...(i)
Again, ar(quad. ABCD) = ar(∆ABC) + ar(∆CDA)
= 2 ar(∆ ABC) ar(∆ABC) = ar(∆CDA)]
∴ ar(∆ABC) = 12
ar(quad. ABCD) ...(ii)
From (i) and (ii), we have:
ar(∆ABD) = ar(∆ABC) = 12
AB ⨯ BD = 12
AB ⨯ CL
⇒ CL = BD
⇒ DC || AB
Similarly, AD || BC.
Hence, ABCD is a paralleogram.
∴ ar(|| gm ABCD) = base ⨯ height = 5 ⨯ 7 = 35 cm2
Answer:
35 cm is the correct answer