formula for quadrilaterals
DESCRIPTION
Quadrilaterals FormulaTRANSCRIPT
General Formula for the Area of Quadrilaterals
Some formulas for area in terms of sides a, b, c, and d, and diagonal lengths e1 and e2 are as follows:
π¨ =π
πππππ π¬π’π§ π½
where ΞΈ is the angle formed between e1 and e2.
π¨ =π
πππ + ππ β ππ β π π ππππ½
where the four sides are labeled such that a2+c2 > b2+d2
ab
cd
C
D
A
Be1
e2
ΞΈ
General Formula for the Area of Quadrilaterals
π¨ = π β π π β π π β π π β π β ππππ πππππ
ππ¨ + πͺ
Where s is the semi perimeter and angles A and C are any two opposite angles of the quadrilateral.
Parallelogram
A parallelogram is a quadrilateral whoseopposite sides are parallel.
A
C
B
D
h (height)
b (base)
Parallelogram
Parallelograms have the followingimportant properties:
1. Opposite sides are equal.2. Opposite interior angles are congruent
( e.g. β π¨ β β π«).3. Adjacent angles are supplementary (
e.g. β π¨ + β πͺ = πππΒ°)4. A diagonal divides the parallelogram
into two congruent triangles ( e.g.Ξπͺπ¨π© = Ξ πͺπ«π©)
5. The two diagonals bisect each other.
A
C
B
D
Diagonals of a Parallelogram
A
C
B
D
a
b
d
ha
h
ΞΈ
By cosine law:
d2 = a2 + b2 β 2 ab cos ΞΈ
If any two parts are given, the relationship among a, h and ΞΈ may be obtained from the right triangle as shown.
Using the other angle, 180Β° - ΞΈ the second diagonal may be obtained by the same formula.
Parallelogram
Perimeter of a Parallelogram: P = 2a + 2b
Area of a Parallelogram:
A = bhA = absin ΞΈ
where b is the length of the base, h is the height , and b are the sides and ΞΈ is any interior angle.
Diagonal of a Rhombus
h
Diagonals of rhombus are perpendicular bisectors.Angle between them is 90Β°.
Using Phytagorean theorem, diagonals may beobtained like in a similar manner like that of aparallelogram.
π =π12
2
+π22
2
b
Diagonal of a Rhombus
h
Where d1 and d2 are the shorter and longerdiagonals respectively, and ΞΈ is the angle opposited1.
π = 2 π‘ππβ1π1π2
b