Formula for Quadrilaterals
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Transcript of Formula for Quadrilaterals
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:
๐จ =๐
๐๐๐๐๐ ๐ฌ๐ข๐ง ๐ฝ
where ฮธ is the angle formed between e1 and e2.
๐จ =๐
๐๐๐ + ๐๐ โ ๐๐ โ ๐ ๐ ๐๐๐๐ฝ
where the four sides are labeled such that a2+c2 > b2+d2
ab
cd
C
D
A
Be1
e2
ฮธ
General Formula for the Area of Quadrilaterals
๐จ = ๐ โ ๐ ๐ โ ๐ ๐ โ ๐ ๐ โ ๐ โ ๐๐๐๐ ๐๐๐๐๐
๐๐จ + ๐ช
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. โ ๐จ โ โ ๐ซ).3. Adjacent angles are supplementary (
e.g. โ ๐จ + โ ๐ช = ๐๐๐ยฐ)4. A diagonal divides the parallelogram
into two congruent triangles ( e.g.ฮ๐ช๐จ๐ฉ = ฮ ๐ช๐ซ๐ฉ)
5. The two diagonals bisect each other.
A
C
B
D
Diagonals of a Parallelogram
A
C
B
D
a
b
d
ha
h
ฮธ
By cosine law:
d2 = a2 + b2 โ 2 ab cos ฮธ
If any two parts are given, the relationship among a, h and ฮธ may be obtained from the right triangle as shown.
Using the other angle, 180ยฐ - ฮธ 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 ฮธ
where b is the length of the base, h is the height , and b are the sides and ฮธ is any interior angle.
Diagonal of a Rhombus
h
Diagonals of rhombus are perpendicular bisectors.Angle between them is 90ยฐ.
Using Phytagorean theorem, diagonals may beobtained like in a similar manner like that of aparallelogram.
๐ =๐12
2
+๐22
2
b
Diagonal of a Rhombus
h
Where d1 and d2 are the shorter and longerdiagonals respectively, and ฮธ is the angle opposited1.
๐ = 2 ๐ก๐๐โ1๐1๐2
b