. A Hinh binh hanh B Hinh vuong C ffinhthoi D Hinh chu nhat
c)Cho S.AB'C CO chieu cao SC, day laA AB'C vuong b B'
(AB' 1 (SBC) nen AB' 1 B'C). Ta c6 AB' = ^ va A C . SC = a.AC ma .a SC = a nen A C = ^ ^ B'C = ^ va SC = ^
3 6 3
Vay F^^^,^. = T ( T - ^ - — ) • — = — Vs.ABc = 6 V S.ABC •
3 ' 2 ' 2 " 6 ' 3 36 6. Tren canh CD la'y E chia trong CD theo ty so —.
n
No'i BE va AE. Mat phang ABE chia khoi tii dian ABCD thanh 2 khoi
chop CO cung chieu cao. Ta dh dang chiing minh -
Hinh 46 Hinh 47
i f ;
7. a) Day lang tm la A ABC c6 difin tich — ^ . Tarn day Ik H vi A ' A =
4
= A ' B = A'C nen A ' H 1 (ABC) va A ' A H = 60° la goc gifta A A ' mat
day. Ta c6 A H = ^ . - ^ = ^ n e n A H ' = A H tg60° = = a 3 2
Vay the tich lang tru A B C . A ' B ' C =
b) BC 1 A H , BC 1 A H => BC 1 ( A A ' H ) => BC 1 A A ' => BC 1 BB' => BCC'B' la hinh chG nhat.
c) A ' A H = 60° => A A ' H = 30° A A ' = 2 A H = 2a => SBCC-B' = 2a'
Tiir E ve EK 1 AA' => BKC la thiet diSn thing cua lang tm. Ta tinh duoc
Vay = a l Vl3 + 2a' = a'(2 + Vo ) don vi dien tich
Ve chop S.ABC. TiT B va B' ha BH 1 (SAC), B'H' ± (SAC). K h i do
BH ^ _SB_ B'H' ~ SB''
Hinh 48
' Dien tich ASAC =-SA.S;G:sin ASC 2 , Dien tich AS A C ' = - SAS C' sin A5C
2 i 1 D o d o ' ^S.ABC _ 3 -S^,.BH SA SC SB . 7- r. r(dpcm). SA SC SB I
Ap dung di^u nky vao bai tapjt s6 5 vdi SC = , SC = a VI.
1 i = 1
~ SA'SC'SB' " n ' 2 ' 3 6 '
Vs.^sc _ SA SC SB
S.ABC
a) A A ' 1 AB, A A ' 1 A C , . \ 1 AC => A B 1 ( A A ' C C ) => B C la ducmg xien c6 hinh chie'u tren, ( A A ' C C ) la A C => B C ' A = 30°.
=> A C i= A B . cotg30°' = AB> /3 ma AB = AC.cotg30° = b V3 => A C = 3b.
b) ^..c.Vc = S A A B C . C C =
= ( l b . b V 3 ) . V % ^ = ^ b ^ ^ = b l V 6
Hinh 49
10. Ha A , H 1 A C ( H e AC) A A , B D can ( do A , B = A,D) BD X A , 0 . Mat khac BD 1 A C BD 1 (A,AO) BD 1 A , H Dan den A , H 1 (ABCD). Dat A, AC = c(? ta c6 he thiic:
a
cos a = coscp c o s y . (*)
That vay: ve A , K 1 A D => H K 1 A.K
AK a AH AK
coscp cos— = . T-