1. The document discusses different geometric shapes and how to calculate various properties of triangles, quadrilaterals, and other shapes using basic formulas like the Pythagorean theorem. 2. Multiple examples are provided to demonstrate calculating lengths of sides and angles using given values and geometric relationships. 3. Formulas used include calculating the area of triangles, summing the areas of component shapes, and deriving side lengths from angles or other sides.

1. F ก F
F F ก F ก
F F ก F F F F
F F F Fก ก F
F F ก ก F ก F
F ก กF
( Pyramid ) ก
F
F F ก F
ก F F ก
F F F F

2. F F F ก ก กก
F กก F F ก
Fก
F F F Fก ก F
F F ก ก F ก F
F ก กF
1 กF F F
F ก ก ก ก ก F F ก ก
F ก F กF F
2 กF F F F ก
3 กF F F F Fก
F ก F F F ก
4 กF F F F F F F
F
5 กF F F F ก ก ก
ก
6 กF F F F F
F Fก

3. F 1 (1) ABC D
DO F F F DO กก ABC O
AO = BO = CO
(2) F ABCDE FO F
F F AO = BO = CO = DO = EO
F กF
(1) (2) FF
DO = (1)
FO = (2)
F 2 F F 12 10
ก ก ABC FF
2
AC = AB2 + BC2
= 122 + 122
= 144 + 144
= 288
AC = 288
= 144 × 2
= 2 12
1
OA = AC
2
1
= ( 2 12 )
2
= 6 2
ก ก AOE FF

4. AE2 = AO2 + OE2
102 = (6 2 )2 + OE2
100 = 72 + OE2
OE2 = 100 72
= 28
OE = 28
= 4×7
= 2 7
- F ก กF F
- F ก กF
F 3 F F F F F 10
12
F = ∆ABC + ∆ABD +
∆ADC
ก F ก F Fก Fก
∆ABC = ∆ABD = ∆ADC
1
F F = 3 × ( × 10 × 12 )
2
= 180
180

5. F 4 F 14
24
ก ∆OXY ก
F OY2 = OX2 + XY2
=
=
OY = 25
ก F F F Fก
1
F = 4 × ( × 14 × 25 )
2
=
=
= 196
=
=

6. ก ก
ก ก (1)
= ×
Fก ก F Fก F
(2) F ก F F
F F F F (3)
F F (4) F 2 F (5)
3 F (6)
ก ก FF
= 3 F
1
=
3
1
= × ×
3

7. 1
=
3
1
= × ×
3
ก
ก F
ก F 3
ก F F Fก
F Fก
F Fก 1
F F ก

8. ก Fก 3 6
F Fก (h)
ก
1 1 1
= × 1×h+ × 2×h+ × 3
3 3 3
×h
1
+ .+ × 6×h
3
1
= × h× ( 1+ 2+ .+ 6)
3
1
= × h× ก
3
FF ก
1
= × ×
3
1
= × ×
3
F ก ก ก ก ก

9. F F F ก F F F F F F
12 20 3 F F F
ก ก กF
1
= × ×
3
= F F F 12
3
= ( 122 )
4
3
= ( 144 )
4
= 36 3
= 36 3
ก F = 20 3
1
= × 36 3 × 20 3
3
= (12 × 20 ) × 3
= 720 ก กF
F F F F 720 ก กF
F F 30
22.5
ก F F
F AB
= 22.5
BC = CD
30
=
2

10. = 15
∆ACD C ก
AD2 = AC2 + CD2
(22.52) = AC2 + (152)
AC2 = (22.52) - (152)
= 506.25 225
= 281.25
∆ABC B ก
AC2 = AB2 + BC2
281.25 = AB2 + (152)
AB2 = 281.25 225
= 56.25
AB = 56.25
∴ = 7.5
1
= × ×
3
1
= × ( 30 × 30 ) × 7.5
3
1
= × 900 × 7.5
3
= 2,250 ก กF
F F F 8 F กF 6
13
ก ก F FF AB = 8
AD = 6
BE = 13

11. DO =
=
(2) ก ก EOB F BO ก EO F
ก (1) BO =
ก ก ABD FF
BD2 =
=
=
BD = 10
BD =
=
= 5
ก ก EOB FF
BE2 =
=
2
EO =
=
EO = 12
1
= × ×
3
=
=
= ก กF