• 瀏覽: 696
• 回覆: 1
 好望角234 尊貴會員 帖子2089 積分2378 註冊時間2007-11-12 [數學] 數學顯求答案 #1 發表於 2021-3-23 09:29 PM  只看該作者 繁 簡 [按此打開] [隱藏] IMG-20210323-WA0002.jpg (21.95 KB)2021-3-23 09:29 PM .postmorevideochannel { margin-top: 10px; display: block; width: 160px; height: 30px; background: url('/images/video_channel_more.png?v=20160829b') no-repeat; font-size: 0; } .postmorevideochannel:hover, .postmorevideochannel:focus { background-position: 0 -30px; } @media (-webkit-min-device-pixel-ratio: 2), (min-resolution: 192dpi) { .postmorevideochannel { background: url('/images/video_channel_more_2x.png?v=20160829b') no-repeat; background-size: 100% auto; } }
引用:

12197412
(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.

[ 本帖最後由 top11 於 2021-3-23 10:18 PM 編輯 ]