Quant 3 Flashcards
(27 cards)
Sum of Interior Angles of a Polygon
(n-2) x 180
Area of a Trapezoid
(Base1 + Base2) x Height / 2
Area of a Parallelogram
Base x Height
Three Dimensions: Volume
The volume of a three-dimensional shape
Volume = Length X Width X Height
Common Right Triangles
3-4-5 or 6-8-10 or 12-16-20
5-12-13 or 10-24-26
8-15-17
Isosceles Triangle
45-45-90
X2 and x2 and x√2
Area of a Triangle
Base x Height / 2
C = Circumference
C = π x d C = 2 x π x r
A = area
A = π x r2
Inscribed Angle
An inscribed angle (30) is equal to HALF of the arc (60) it intercepts, in degrees…
Inscribed Triangle
If one of the sides of an inscribed triangle is a DIAMETER of the circle, then the triangle MUST be a right triangle.
Volume of a Cylinder
V = π x r2 x h
Slope = Rise/Run
The slope of a line is equal to = y2 - y1 / x2 - x1
Two other points on the line may have a different rise and run, but the slope would be the same. The “rise over run” would always be the same BECAUSE a line has a CONSTANT slope.
Area of Rhombus
Diagonal1 x Diagonal2 / 2
Maximum Area of a Quadrilateral
Rule: Of all quadrilaterals with a given perimeter, the square has the largest area.
Corollary (doğal sonucu): Of all quadrilaterals with a given area, the square has the minimum perimeter.
Both of these principals can be generalized for N sides:
“A regular polygon with all sides equal will maximize area for a given perimeter and minimize perimeter for a given area”
Maximum Area of a Parallelogram or Triangle
If you are given two sides of a triangle or parallelogram, you can maximize the area by placing those two sides perpendicular to each other.
Triangles and Area
The area of an EQUAL triangle with a side of length S is equal to:
S2√3 ÷ 4
***If two similar triangles have corresponding side lengths in ratio A:B, then their areas will be in ratio A2:B2
Main Diagonal of a Cube
d = s√3
Main Diagonal of a Rectangular Solid
“Deluxe” Pythagorean Theorem:
d2 = x2 + y2 + z2
Revolution = Circumference
If you were to place a point on the edge of the wheel, it would travel one full circumference in one revolution.
For example, if a wheel spins at 3 revolution per second, a point on the edge travels a distance equal to 3 circumferences per second.
Cylinders and Surface Area
SA = 2 circles + rectangle = 2(Ωr)2 + 2Ωrh
Parallel Lines have Equal Slopes
M1 = M2
Perpendicular Lines have Negative Reciprocal Slopes
-1/m1 = m2
OR
m1.m2 = -1
The MIDPOINT between point A(x1 , y1) and point B(x2 , y2)
x1 + x2 / 2 , y1 + y2 / 2)
