The Regular Polygon
Rhombus is a quadrilateral with all sides equal (equilateral). Rectangle is a quadrilateral with all included angles are equal (equiangular). Square is both equilateral and equiangular, thus square is a regular polygon. Regular polygons are polygons with all sides equal and all included angles equal. Meaning, regular polygons are both equilateral and equiangular.

Properties of regular polygons

1. The center of the circumscribing circle, the center of inscribed circle, and the center of polygon itself are coincidence. 2. All sides of regular polygon are equal in length; it is denoted by x in the figure. 3. All included angles are equal; it is denoted by β.

4. All external angles α, are equal.
5. Central angles of each segment are equal; it is denoted by θ. 6. The apothem is the radius of the inscribed circle, r.
7. The number of sides is equal to the number of vertices, both are denoted by n. 8. Diagonals of regular polygon will cross each other at the center. Length of diagonals is equal to the diameter of the circumscribing circle. 9. Segment of regular polygon is an isosceles triangle whose equal sides are radius of circumscribing circle; its area is denoted by A1.

Formulas for a Regular Polygon
Area of one segment, A1

Total area, A

Perimeter, P

Central angle, θ

Exterior angle, α

Interior angle, β

Where
A1 = area of one segment
A = total area
x = length of side
r = radius of the inscribed circle (apothem)
R = radius of the circumscribing circle
n = number of sides
θ = central angle
α = exterior angle
β = interior angle

Derivation of formula for volume of a frustum of pyramid/cone

Frustum of a pyramid and frustum of a cone

The formula for frustum of a pyramid or frustum of a cone is given by

Where:
h = perpendicular distance between A1 and A2 (h is called the altitude of the frustum) A1 = area of the lower base
A2 = area of the...

...Plane and Solid Geometry Formulas
ASIAN DEVELOPMENT FOUNDATION COLLEGE
Tacloban City Given four sides a, b, c, d, and sum of two opposite angles:
Prepared by: RTFVerterra
10 sides 11 sides 12 sides 15 sides 16 sides = = = = = decagon undecagon dodecagon quindecagon hexadecagon
RADIUS OF CIRCLES Circle circumscribed about a triangle (Cicumcircle)
A=
(s − a)(s − b)(s − c)(s − d) − abcdcos2 θ
s=
a+b+c+d 2 ∠A + ∠C ∠B + ∠D θ= or θ = 2 2
The content of this material...

...The dimensions of a regular rectangular solid are in the ratio of 1:6:6 and its volume is 562.5cm3. Find the volume of a cube whose surface are equal to the surface of the rectangular solid.
V = 562.5 = l ⋅ w ⋅ h
36x3 = 562.5
x = 2.5cm
∴2.5:15:15
TSA▭= 2[2(2.5)(15)] + 2(15)(15) = 600cm2
∵ TSA□ = TSA▭
TSA□ = 600 = 6s2
s = 10
V = (10)3 = 1000cm3
10. An object in which the ends are regular hexagons was cut from a cylindrical wooden...

...right prism is an equilateral triangle whose sides measure in 4in. two of the lateral edges of the prism are congruent, each measuring 9in. long. If one edge of the upper base measures 5in., find the possible lengths of the third lateral edge of the solid.
5= 42+9-x2
5= 16+81-8x+x2
(52=x2-18x+)2
25= x2-18x+97
x2-18x+72= 0
(x-6)(x-12)= 0
x=6
x=12 Answer = 6in or 12in
#13. Suppose two cylindrical...

...1.) the diagonal of a rectangle is 25 meters long and makes an angle of 36 degree with one side of the rectangle. Find the area and the perimeter of the rectangle.
2.) A side of a square is 16 inches. The midpoints of its sides are joined to form an inscribed square. Another is drawn in such a way that its vertices would lie also at the midpoints of the sides of the second square. This process is continued infinitely. Find the sum of the areas of these infinite squares.
3.) A rectangle...

... * Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
As the volume of a cube is the third power of its sides , third powers are called cubes, by analogy with squares and second powers.
A cube has the largest volume among cuboids (rectangular boxes) with a given surface area. Also, a cube has the largest volume among cuboids with the same total linear size (length+width+height).
*...

...What are factors that affect your computer performance
Name: Pequeña, Anthony Pol S.
Section:AR32FA1
What affects a computers performance
Overall, the performance of a computer is dependant on how well it works together as a whole. Continually upgrading one part of the computer while leaving outdated parts installed will not improve performance much, if at all. Below, we discuss some of the most important parts of the computer regarding it's speed and computing power....

...Project
In
Arts, Man and Society
Project
In
Arts, Man and Society
Submitted to:
Ms. Glenn Dale Pobadora
Submitted to:
Ms. Glenn Dale Pobadora
Submitted by:
Jira L. Hora
Ma. Christina Daganato
Gilling Marie Andrea M. Ares
Lovely Rose F. Dablio
Prudence Mae P. Cailing
Submitted by:
Jira L. Hora
Ma. Christina Daganato
Gilling Marie Andrea M. Ares
Lovely Rose F. Dablio
Prudence Mae P. Cailing
ESSAYS:
Jira L. Hora –
I was really amazed when I saw the Architecture Church of Immaculate...

...used together with the book Electrical Circuits 2nd Edition by Charles S. Siskind. This is one attempt to provide the students of Garcia College of Technology taking up the Electrical engineering program another reference material for them to have a solid foundation of the course and a confident mind going into the other major courses.
viii
RECOMMENDATIONS
The following recommendations are presented by the author.
1. This manual should be used by students taking up...

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