Jajar genjang
a
{\displaystyle a}
t
{\displaystyle t}
Jajar genjang atau jajaran genjang (bahasa Inggris : parallelogram dua dimensi yang dibentuk oleh dua pasang rusuk yang masing-masing sama panjang dan sejajar dengan pasangannya, dan memiliki dua pasang sudut yang masing-masing sama besar dengan sudut di hadapannya.
Jajar genjang termasuk turunan segiempat yang mempunyai ciri khusus.
Jajar genjang dengan empat rusuk yang sama panjang disebut belah ketupat .
Rumus jajar genjang
Keliling
K
=
2
⋅ ⋅ -->
(
s
1
+
s
2
)
{\displaystyle K=2\cdot (s1+s2)}
Luas
L
=
a
⋅ ⋅ -->
t
{\displaystyle L=a\cdot t}
Tinggi
h
a
=
b
⋅ ⋅ -->
sin
-->
(
α α -->
)
{\displaystyle h_{a}=b\cdot \sin(\alpha )}
h
b
=
a
⋅ ⋅ -->
sin
-->
(
β β -->
)
{\displaystyle h_{b}=a\cdot \sin(\beta )}
Diagonal
e
=
a
2
+
b
2
− − -->
2
⋅ ⋅ -->
a
⋅ ⋅ -->
b
⋅ ⋅ -->
cos
-->
(
β β -->
)
=
a
2
+
b
2
+
2
⋅ ⋅ -->
a
⋅ ⋅ -->
b
⋅ ⋅ -->
cos
-->
(
α α -->
)
{\displaystyle {\begin{array}{ccl}e&={\sqrt {a^{2}+b^{2}-2\cdot a\cdot b\cdot \cos(\beta )}}\\&={\sqrt {a^{2}+b^{2}+2\cdot a\cdot b\cdot \cos(\alpha )}}\end{array}}}
f
=
a
2
+
b
2
− − -->
2
⋅ ⋅ -->
a
⋅ ⋅ -->
b
⋅ ⋅ -->
cos
-->
(
α α -->
)
=
a
2
+
b
2
+
2
⋅ ⋅ -->
a
⋅ ⋅ -->
b
⋅ ⋅ -->
cos
-->
(
β β -->
)
{\displaystyle {\begin{array}{ccl}f&={\sqrt {a^{2}+b^{2}-2\cdot a\cdot b\cdot \cos(\alpha )}}\\&={\sqrt {a^{2}+b^{2}+2\cdot a\cdot b\cdot \cos(\beta )}}\end{array}}}
Sudut interior
α α -->
=
γ γ -->
,
β β -->
=
δ δ -->
,
α α -->
+
β β -->
=
180
∘ ∘ -->
{\displaystyle \alpha =\gamma ,\quad \beta =\delta ,\quad \alpha +\beta =180^{\circ }}
Persamaan jajar genjang
e
2
+
f
2
=
2
⋅ ⋅ -->
(
a
2
+
b
2
)
{\displaystyle e^{2}+f^{2}=2\cdot (a^{2}+b^{2})}
Elemen geometri menurut dimensi Besaran geometri menurut dimensi Istilah dasar lain Bangun 2 dimensi Bangun 3 dimensi
