1. No category


 ‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬
٤
- ٦٤ -
 ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬
 
 W‫א‬‫א‬
 W‫א‬‫א‬‫א‬
E‫א‬‫א‬ J‫א‬ J‫א‬‫א‬F‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬
E‫א‬ J‫א‬ J‫א‬‫א‬ J‫א‬F‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
•
•
•
•
 
 K٪٨٠‫א‬‫א‬W‫א‬‫א‬‫א‬
 
W‫א‬‫א‬
‫א‬‫א‬‫א‬
١١٦
‫א‬‫א‬‫א‬‫א‬
 ‫א‬
 

 ‫א‬‫א‬‫א‬‫א‬
 
 ‫א‬‫א‬K١
 W‫א‬‫א‬‫א‬‫א‬

 K‫• א‬
 K‫א‬‫• א‬
 ‫א‬‫א‬K١{١
‫א‬‫א‬ ،‫א‬‫א‬
 W‫א‬
 KEF‫א‬ Ea
 K‫א‬ Eb
 K‫א‬‫א‬‫ א‬Ec
 ‫א‬‫א‬K١{١{١
  W‫א‬‫א‬‫א‬
D
A

  P = 2 EF
= 2( AB + AD )
 


F
C
H
B
 A = DH × CB
 W‫א‬
  A = ‫א‬‫א‬ × ‫א‬
or
A = DF × AB 
 
 K‫א‬‫א‬‫א‬ •
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬
‫א‬‫א‬‫א‬
١١٦
‫א‬‫א‬‫א‬‫א‬
 ‫א‬
 

‫א‬‫א‬K 8 cm, 14cm ‫א‬W١
 K 5cm ‫א‬‫א‬
 W‫א‬



 P = 2 EFW‫א‬‫א‬
  P = 2(8 + 14) = 44 cm 


 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬
  A = ‫א‬ × ‫א‬ = 5 × 14 = 70 cm 2 
D





 ‫א‬K٢{١{١
A
 K‫א‬‫א‬
C
 ‫• א‬
ow
o
l
B

= 2( AB + AD )
  P = 2 [ (w) ‫א‬H (l ) ‫]א‬


 ‫• א‬
= AB × AD
  A = (w) ‫א‬ × (l ) ‫א‬


 K‫א‬K11cm 17 cm W٢
  P = 2 [ (w) ‫א‬H (l ) ‫]א‬ = 2(11 + 17) = 56 cm 
  A = (w) ‫א‬ × (l ) ‫א‬ = 11 × 17 = 187 cm 2 
W‫א‬
W‫א‬
W‫א‬

 K‫א‬K16 ‫א‬، 320 cm 2 W٣
 
W‫א‬
(l ) ‫א‬ = ‫א‬ ( A) ÷ (w) ‫א‬
 l =
320
= 20cm 
16





  (P) ‫א‬
  P = 2 [ (w) ‫ א‬+ (l ) ‫ = א‬2(16 + 20) = 72 cm ]
‫א‬‫א‬‫א‬
١١٦
‫א‬‫א‬‫א‬‫א‬
 ‫א‬
 

 K‫א‬KK 7 cm W٤
 W‫א‬
  L = 3 × 7 = 21cm W (L) ‫א‬‫א‬
  P = 2 [ (w) ‫א‬H (l ) ‫]א‬ = 2(7 + 21) = 56 cm 
  A = (w) ‫א‬ × (l ) ‫א‬ = 7 × 21 = 147 cm 2 
W‫א‬
W‫א‬



 ‫א‬K٣{١{١


o
  P = 4 ×  (l ) ‫א‬ = 4 l 
o
W (P) ‫א‬ •
  A = (l ) ‫ × א‬ (l ) ‫ = א‬l 2 W ( A) ‫א‬ •
o
‫א‬K 9cm W٥
 K
l
 W‫א‬
o
  P = 4 ×  (l ) ‫א‬ = 4 l = 4 × 9 = 36 cm W‫א‬
  A = (l ) ‫ × א‬ (l ) ‫ = א‬l 2  = 9 2 = 81cm 2 W‫א‬
 K‫א‬ 48 cm W٦
 W‫א‬
  l = P ÷ 4 = 48 ÷ 4 = 12cm W‫א‬
  A = l 2 = (12) 2 = 144 cm 2 W‫א‬


 K‫א‬ 49cm 2 W٧
 W‫א‬
  l = A = 49 = 7 cm  W‫א‬
  P = 4 × (l ) ‫א‬ = 4 l = 4 × 7 = 28 cm 
A
•
o
l
•
D
o
H
C

 ‫א‬K٤{١{١
  W‫א‬‫א‬‫א‬
B
o
o
W‫א‬

 K‫א‬ Ea
K‫א‬ Eb
‫א‬‫א‬‫א‬
١١٦
‫א‬‫א‬‫א‬‫א‬
 ‫א‬
 

 K‫א‬ Ec
 K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ Ed
  P = 4 ×  (l ) ‫א‬
‫א‬ •
  A = DC × AH
‫א‬ •
 ‫א‬ × ‫א‬ = ‫א‬
1
2
 ‫א‬‫א‬‫א‬
  A = E‫א‬‫א‬ × ‫א‬‫א‬F




‫א‬K 5cm ‫א‬13cm W٨
 K
  P = 4 × (l ) ‫א‬ = 4 l = 4 × 13 = 52 cm 
  A = ‫א‬ × ‫א‬ = 13 × 6 = 78 cm 2 
 W‫א‬
W‫א‬
W‫א‬


 ‫א‬‫א‬‫א‬ 4m, 7 m W٩
 ‫א‬‫א‬،15
1
2
 14 × 15 = 210 
1
2
  A = E‫א‬‫א‬ × ‫א‬‫א‬F = (4 × 7) = 14 m 2 ‫א‬

W‫א‬

o


 
 ‫א‬K٥{١{١
 ‫א‬


o
 W‫א‬
 K‫א‬‫א‬‫א‬
•
•
  P = ‫א‬‫א‬W‫א‬ •
‫א‬ •
  A = ‫א‬ × ‫א‬‫א‬
  A = ‫א‬ × ‫א‬ W
 K‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
١١٦
‫א‬‫א‬‫א‬‫א‬
 ‫א‬
 

 K‫ א‬K11cm ‫א‬17cm ‫א‬W١٠
  A = ‫א‬ × ‫א‬ = 17 × 11 = 187cm 2 
W‫א‬

 ‫א‬K٢{١
 180o ‫א‬‫א‬‫א‬‫א‬
 W‫א‬
A
 K‫א‬ Ea
  K‫א‬ Eb
o
 K‫א‬ Ec
o
K‫א‬‫א‬‫א‬‫ א‬Ed
‫א‬‫א‬‫א‬‫א‬
C
B
H
 ∠CAB ‫א‬‫א‬ CB ‫א‬ A ‫א‬
 ‫א‬ •
  P = AB + BC + CA ‫א‬ 
1
2
 ‫א‬ •
 W‫א‬‫א‬
1
2
  A = × ‫א‬ × ‫א‬‫א‬ = × CB × AH 


 K 8 cm ‫א‬12 cm ‫א‬‫א‬W١١
1
2
 W‫א‬
1
2
  A = × ‫א‬ × ‫א‬‫א‬ = × 12 × 8 = 48 cm 2 W‫א‬

 K 8 cm ‫א‬‫א‬‫א‬K 7cm ‫א‬W١٢
 K
 W‫א‬
  P = 3 × 7 = 21cm W‫א‬
 
A=
7×8
= 28 cm 2 W‫א‬
2


 
‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬
١١٦
 ‫א‬
 

 ‫א‬‫א‬K٣{١
‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬

  ‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬  K
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬ J
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬ J
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ J
  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ J
r
‫א‬
d
‫א‬
  P = 2πr 
 ‫א‬‫א‬ •

W r ‫א‬‫א‬‫א‬
E‫א‬‫א‬F‫א‬‫א‬ π 
‫א‬
 
22
≈ 3,142 
7
 




 W‫א‬‫א‬ •
  A = πr 2  W r ‫א‬‫א‬‫א‬

 K‫א‬ 2.8 m ‫א‬‫א‬W١٣
 W‫א‬
2.8
= 1.4 m W‫א‬
2
W‫א‬
  P = 2πr = 2 × 3.14 × 1.4 ≈ 8.8 m 
 r =
  A = πr 2 = 3.14 × (1.4) 2 ≈ 6.2 m 2 
W‫א‬



 ‫א‬ 66 m ‫א‬‫א‬W١٤
 W‫א‬
  r = 66 ÷ 3.14 ≈ 21 m W‫א‬
  A = πr 2 = 3.14 × (21) 2 ≈ 1385 m 2 
W‫א‬


‫א‬‫א‬‫א‬
١١٦
‫א‬‫א‬‫א‬‫א‬
 ‫א‬
 

 
 ‫؟‬، 6 cm ‫א‬15 cm ‫א‬‫א‬ E١
‫א‬‫א‬‫א‬‫א‬،12 cm ‫א‬‫א‬ E٢
 K10 cm ‫א‬
،10 cm ‫א‬، 50 cm ،‫א‬‫א‬ E٣
 ‫؟‬12.35 m 2 ‫א‬‫א‬
A
‫א‬K BCDE ، ABCDE ‫א‬‫א‬‫ א‬E٤
E
 CD   8 m   AC    ‫א‬ ABCDE 
B
K 6 m 
8m
 
 
D
 
C
6m
‫א‬ K       ‫א‬ ‫ א‬E٥
5m
K‫א‬‫א‬
4m
4m
 
 
6m
 
4m
 
W‫א‬‫א‬ E٦
2.5cm
5cm
70m
2.5cm
1cm
20m
6cm
4cm
25m
2cm
2cm
4cm
25m
20m
3cm
3cm
40m
4cm
 
‫א‬‫א‬‫א‬
١١٦
‫א‬‫א‬‫א‬‫א‬
 ‫א‬
 

‫א‬   ‫א‬‫א‬  ‫א‬ ‫א‬ ‫א‬ ، 42 cm     ‫א‬ ‫א‬ E٧
K 560
8cm
‫א‬‫א‬‫א‬‫א‬‫ א‬E٨
 
 
8cm
 
    ، 60 m   ‫א‬   E٩
8cm
‫؟‬‫א‬،
K140 cm ‫א‬‫א‬ 220 cm ،
E١٠
W‫א‬‫א‬‫א‬‫א‬‫א‬
E١١
 ‫؟‬‫؟‬‫א‬
6cm
5cm
4cm
1cm
3cm
 
 ،‫א‬ ‫א‬      ، 27 m    ‫א‬  
E١٢
K127 cm ‫א‬‫א‬، 27 m , 39m ‫א‬،‫א‬
E١٣
‫؟‬ 31.4 cm ،‫א‬‫א‬
E١٤
‫א‬‫א‬‫א‬K 81cm 2 ‫א‬
E١٥
K12 m  17 m ‫א‬‫א‬،‫א‬
E١٦
‫؟‬‫א‬‫א‬‫א‬K10 m 
‫؟‬‫א‬‫א‬‫א‬
K‫א‬
K‫א‬
‫א‬‫א‬‫א‬
١١٦
‫א‬‫א‬‫א‬‫א‬
 ‫א‬
 

 ‫א‬‫א‬‫א‬K٢
 
 K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫• א‬
‫א‬‫א‬‫א‬W‫א‬‫• א‬
 K‫א‬
‫א‬‫א‬WE‫א‬F‫א‬‫• א‬
 ‫א‬    ‫א‬ ‫א‬        ‫א‬ ‫א‬ 
 K‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬ •
 ‫א‬‫א‬K١{٢
‫א‬،

 K‫א‬‫א‬‫א‬
 K h ‫א‬ w ‫א‬، l ‫א‬W‫א‬‫א‬
W‫א‬‫א‬‫א‬‫• א‬
  A = 2(l × w + l × h + w × h) 
V = l × w × h ‫א‬‫א‬ •
h
K 7cm, 9cm, 11cm ‫א‬‫א‬W١٥ 
‫א‬
w
‫א‬
l
 K‫א‬‫א‬
 W‫א‬
  w = 7, l = 9, h = 11 ‫א‬

W‫א‬‫א‬
  A = 2(l × w + l × h + w × h) = 2(9 × 7 + 9 × 11 + 7 × 11) = 2(63 + 99 + 77) = 478 cm 2
 W‫א‬
V = l × w × h = 9 × 7 × 11 = 693 cm3 
 ‫א‬K٢{٢
 ،
K‫א‬‫א‬
l
‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬
١١٦
 ‫א‬
 

  l EF‫ א‬‫א‬
  A1 = 4l 2 
‫א‬ •
  A2 = 6l 2  ‫א‬ •
  V = l 3 

W
‫א‬‫א‬‫א‬K 7cm ‫א‬W١٦
 K
 W‫א‬
  A1 = 4l 2 = 4(7) 2 = 196 cm 2  W‫א‬‫א‬
  A2 = 6l 2 = 6(7) 2 = 294 cm 2 W‫א‬‫א‬
  V = l 3 = 7 3 = 343 cm 3 

W‫א‬
  ‫א‬‫א‬K٣{٢
 K‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫• א‬

W h ‫א‬ r ‫א‬‫א‬‫א‬‫א‬
  A = 2πr 2 + 2πrh = 2πr (r + h) 



 ‫א‬‫א‬ •

  v = πr 2 h W r ‫א‬‫א‬‫א‬
‫א‬K11cm ‫א‬ 9cm ‫א‬W١٧
 K
 W‫א‬
  A = 2πr (r + h) = 2 × 3.14 × 9 × (9 + 11) = 1130.97 cm 2 W‫א‬‫א‬‫א‬
  v = πr 2 h = 3.14 × (9) 2 × 11 = 2797.74 cm 3 

W‫א‬‫א‬
 
 
 
‫א‬‫א‬‫א‬
١١٦
‫א‬‫א‬‫א‬‫א‬
 ‫א‬
 

 ‫א‬K٤{٢
‫א‬، r ‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫• א‬
  W h ‫א‬ r ‫א‬‫א‬‫א‬
2
3
  Al = πrh 
 ‫א‬‫• א‬
W h ‫א‬ r ‫א‬‫א‬‫א‬
h
2
3
  AT = πrh + πr 2  
r
 W‫א‬ •
 h ‫א‬ r ‫א‬‫א‬
 W
1
3
 V = πr 2 h 

‫א‬ h = 11cm ‫א‬  r = 14 cm ‫א‬W١٨
 K‫א‬‫א‬
2
3
 W‫א‬
2
3
  Al = πrh = × 3.14 × 14 × 11 = 322.38 cm 2 W‫א‬‫א‬
W‫א‬‫א‬
  AT = πrh + πr 2 = πr ⎛⎜ h + r ⎞⎟ = 3.14 × 14 × ⎛⎜ × 11 + 14 ⎞⎟ = 43.96 × 21.34 = 937.81cm 2
2
3
2
⎝3
2
⎝3
⎠
 

⎠
1
1
  V = πr 2 h = × 3.14 × (14) 2 × 11 = 2256.61cm3
3
3
W‫א‬
 ‫א‬K٥{٢ •
‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
١١٦
‫א‬‫א‬‫א‬‫א‬
 ‫א‬
 

 
 
‫א‬‫• א‬
  A = 4πr 2  W r ‫א‬‫א‬
‫א‬ •
4
3
  V = π r 3  W r ‫א‬‫א‬
r
‫א‬K17 cm W١٩
 K‫א‬
 W‫א‬
 W‫א‬‫א‬
  A = 4πr 2 = 4 × 3.14 × 17 2 = 3631.68 cm 2
 
  A = 4 πr 3 = 4 × 3.14 × (17) 3 = 2.57953cm3
3
3

 
W‫א‬
‫א‬‫א‬‫א‬
١١٦
‫א‬‫א‬‫א‬‫א‬
 
 ‫א‬

 
K 8 m ‫א‬،13 m ،17 m ،‫א‬‫א‬ E١
‫؟‬‫؟‬‫א‬‫א‬
،‫א‬‫א‬،، 850cm 3 ، E٢
‫א‬K11cm ،13 cm ،‫א‬‫א‬
‫؟‬‫א‬‫א‬
‫א‬، 25 cm  84 cm ،‫א‬ E٣
‫؟‬‫א‬‫א‬K،‫א‬‫א‬، 5 cm ،
‫א‬     9 cm  ‫א‬     19 cm        E٤
K‫א‬K13 cm ‫א‬‫א‬
‫א‬K 27 cm ‫א‬ E٥
2
‫א‬13 m ‫א‬
17
‫א‬13 cm ‫א‬‫א‬‫ א‬E٦
‫؟‬‫א‬
K
   7 cm   ‫א‬    ‫א‬ K‫א‬   ‫א‬‫א‬   E٧
K12 cm ‫א‬‫א‬‫א‬‫א‬
 C2  ‫א‬‫א‬    ‫א‬ K  C1 , C2 ‫א‬     E٨
 V1 K C1  ‫א‬‫א‬ h ‫א‬‫א‬ C1 ‫א‬
 C2 ‫א‬‫א‬‫א‬‫א‬K‫א‬ V3  C2 ‫א‬‫א‬ V2  C1 ‫א‬‫א‬
KV2 = V1 + V3 ‫א‬ h 
C1
C2