Area & Volume MCQ

Alex

2015-01-05 5:48 am

In the figure, ABCD is a parallelogram. E and F are the mid-points of AD and AB respectively. If CE is perpendicular EF, CE = 3 cm and the area of
△AEF = 2 cm2, find the perimeter of △CEF.
https://www.flickr.com/photos/130230543@N06/16007319270/
A.10.5 cm
B.12 cm
C.13.5 cm
D.15 cm

回答 (1)

用戶2053

2015-01-05 7:06 am

✔ 最佳答案

圖片參考：https://s.yimg.com/lo/api/res/1.2/w92fgNn8uQqXDpqRWC58Ww--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/https://farm8.staticflickr.com/7547/16007319270_c797e09b08_o.jpg

△BCF = 2△AEF = 2(2) = 4 cm² = △CDE

Parallelogram ABCD = 2△ABC = 2(2△BCF) = 2(2 × 4) = 16 cm²
△BCF + △CDE + △AEF + △CEF = 16
4 + 4 + 2 + △CEF = 16
△CEF = 6 cm²
CE × EF / 2 = 6
3 × EF / 2 = 6
EF = 4 cm

The perimeter of △CEF = CE + EF + CF = 3 + 4 + √(3² + 4²) = 12 cm
The answer is B.

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