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Title: Plane and Solid Geometry
Description: shortcut formulas for plane and solid geometry
Description: shortcut formulas for plane and solid geometry
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PLANE AND SOLID GEOMETRY
PLANE GEOMETRY
Plane geometry is all about shapes, like lines, circles and triangles that are drawn on same flat surface called plane
...
Exterior angle:
θ=
360 o
n
Area:
A=
Perimeter:
1 2
1
R (sin θ) n = xr n
2
2
P = (x)(n)
Interior angles =
n−2
* 180o
n
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com
PLANE AND SOLID GEOMETRY
CIRCLE
Sector of a circle
Segment of a circle
A = A Sector + A Triangle
1 2
r θrad
2
A=
D2
A = πr 2 = π
4
Arc:
S = rθ rad
A = A Sector − A Triangle
1
1
A = r 2 θ rad − r 2 sin θ
2
2
A=
1 2
1
r α rad + r 2 sin θ
2
2
Circumference = 2πr = πD
Note: 180o = 2π rad
ELLIPSE
PARABOLIC SEGMENT
A = πab
A=
2
bh
3
Circle Escribed (Excircle) about a triangle
Circle circumscribed about a triangle
Radius of escribed circle:
Radius of circumscribed circle:
r =
abc
4A T
ra =
AT
s−a
Circle Circumscribed about a Quadrilateral
Circle inscribed in a triangle
Radius of circumscribed circle:
Radius of inscribed triangle:
r =
AT
s
A quad =
a+b+c
s=
2
s=
r=
A quad
s
abcd
a+b+c+d
2
SOLID GEOMETRY
Solid geometry treats shapes and figures that do not lie in the same plane
...
Prism
Prism is a polyhedron whose base and ends have the same size and
shape extended in parallel planes whose sides are a parallelogram
...
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Title: Plane and Solid Geometry
Description: shortcut formulas for plane and solid geometry
Description: shortcut formulas for plane and solid geometry