Increase by k%: multiply be (1+k%) Decrease by k%: multiply by (1-k%)

Mode 2-0: linear system of two equations

Mode 2-1: linear system of three equations

Mode 2-2: quadratic equation

To convert deg to rad:

(Deg)(𝝅

𝟏𝟖𝟎) =

𝑹𝒂𝒅

𝑎

sin𝐴=

𝑏

sin𝐵=

𝑐

sin𝐶

𝑎2 = 𝑏2 + 𝑐2 − 2𝑏𝑐 cos𝐴

Each interior angle of a regular polygon:

𝟏𝟖𝟎(𝒏−𝟐)

𝒏

Area of triangle ABC:

= 𝟏

𝟐(base)(height)

=𝟏

𝟐a.b.sin C

= √𝑘(𝑘 − 𝑎)(𝑘 − 𝑏)(𝑘 − 𝑐) where k=half perimeter

Area of a trapezoid:

(𝐛𝟏+𝐛𝟐)𝐡

𝟐

Area of parallelogram ABCD:

1. (base)(height) 2. (AB)(BC)sin(B) 3. (AB)(AD)sinA

4. 1

2(AC)(BD)sinO

Area of a circle of radius r: 𝝅𝒓𝟐 Perimeter of a circle of radius r: 2πr

Area of regular n-sided polygon= 1

4𝑛𝑆2÷ tan(

180

𝑛)

S: side length

Arc length: Rϴrad ϴ: central angle

Sector area: 1

2R2θrad

Segment area: 1

2R2(θrad − sinθ)

P0=2(L+w)+2Y Y: depth of the bay P=P0±8(HA)

Area of a uniform strip =(Pmid)(width of strip) Volume of a prism ring=(Pmid)(width)(height) Area of formwork (both sides)= (Pin+Pout)(height)= 2(Pmid)(height)

Central angle=subtended arc (in angle measure)

Inscribed angle= half of the subtended arc (angle measure)

Roofer’s theorem:

actualroofarea =projectedarea

cos(α)

Where: α = tan−1(pitch)

b2

b1

h

O

A B

CD

Right Prisms and cylinders: Right Pyramids and cones:

Lateral area: Perimeter of the baseheight (Perimeter of the base)(slant height)(1/2)

Volume: The area of the baseheight (The area of the base)(height)(1/3)

Total area: Lateral area+2(area of the base) Lateral area+area of the base

Right Pyramidal/conical frustums:

Lateral area )(

221 pp

sh , where sh=slant height of the frustum, P1, P2 are the perimeter of the

top and bottom bases

Total area

Lateral area+Area of the top base+Area of the bottom base

Volume

accurate :h

3(A1 A2 A1A2 ) , where A1,A2 are the areas of the top and bottom

base approximate: (the area of the middle section)(height)

Formulas for spherical surfaces:

Sphere of radius R

volume 4

3R3

surface area 4R2

Dome of height h, base radius r, and sphere radius of R

volumeh

6(h2 3r 2 ) Rharealateral 2

Spherical Frustum of height h. a,b: radius of top base and bottom base, R: sphere radius

volume1

6h(3a2 3b2 h2 ) Rharealateral 2

Spherical Lune of angle

volume 2

3radR3

22 Rarealune rad

Spherical Sector R= radius of sphere, h= dome height

volume 2

3R2h

Totalarea R(2h r)