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Areas of Parallelograms and Triangles
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16/07/2021 4:38 pm
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In Figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F.
Show that
(i) ar(△ACB) = ar(△ACF)
(ii) ar(AEDF) = ar(ABCDE)
1 Answer
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16/07/2021 4:40 pm
(i) △ACB and △ACF lie on the same base AC and between the same parallels AC and BF.
∴ ar(△ACB) = ar(△ ACF)
(ii) ar(△ACB) = ar(△ACF)
⇒ ar(△ACB) + ar(△ACDE) = ar(△ACF) + ar(△ACDE)
⇒ ar(ABCDE) = ar(△AEDF)