好望角234 2021-3-23 21:29
[attach]12197412[/attach]
top11 2021-3-23 22:17
[quote]原帖由 [i]好望角234[/i] 於 2021-3-23 09:29 PM 發表 [url=https://www.discuss.com.hk/redirect.php?goto=findpost&pid=533262485&ptid=29788824][img]https://www.discuss.com.hk/images/common/back.gif[/img][/url]
12197412 [/quote]
(a)
ΔAFE ~ ΔCFB (AAA)
BC = AD = AE + ED
so AE : BC = AE : AD = 4 : 5
Area of ΔAFE : Area of ΔCFB = 4² : 5² = 16 : 25
(b)
The area of Area of ΔAFE is 16 cm².
By (a), the area of Area of ΔCFB is 16 ÷ 16 × 25 = 25 cm².
By the corresponding sides of similar triangles, AF : FC = AE : BC = 4 : 5
Area of ΔABF : Area of ΔFBC = 4 : 5
(because they share the same base AC (and same height))
That is, the area of ΔABF = 25 ÷ 5 × 4 = 20 cm²
Therefore, the area of ΔABC = 20 + 25 = 45 cm²
Thus, the area of the parallelogram ABCD = 2 × 45 = 90 cm².
[[i] 本帖最後由 top11 於 2021-3-23 10:18 PM 編輯 [/i]]