數學知識交流---簡單幾何(1)

1.
∵rectangle ABEF and parallelogram CDEF have same base and height
∴area of rectangle ABEF = area of parallelogram CDEF
∵S1 and S2 can be obtained by subtracting the common space from the rectangle ABEF and the parallelogram CDEF respectively
∴area of S1 = area of S2
Hence area of S1 - area of S2 = 0

2.
　area of ΔADC
= 1/2 × AD × AC sin A
= 1/2 × 5AE × 3AB sin A
= 15 × 1/2 × AE × AB sin A
= 15 × area of ΔABE
= 15 × 1 cm²
= 15 cm²

3.
Combine the two part of orange regions will become a right angle triangle region
∴area of the orange regions
= 4/2
= 2

1. S1=AB x AF- area of the triangle FE?
S2=FE x AF- area of the triangle FE?
S1-S2=0

2.No such triangle!!

3.Area of AD=Area of AC
∴Area of orange region=4 x 1/2 =2

YES,ABCD is a rectangle

2011-05-16 17:20:55 補充：
Oh neo ! It should be

ABEF is a rectangle

My mistake , sorry

ABCD is a rectangle ??

2011-05-18 17:36:16 補充：
no.2, the same problem, I don't know what is triangle ABC.

AD = EF ??