Chapter 11.1-11.3 Flashcards
Herons Formula
Sides of the triangle be (a, b, c) and let s (semi-perimeter) be as follows: s= 1/2(a+b+c) then the area of a triangle is as follows:
A= square root (s(s-a) (s-b) (s-c)
Perimeter
Some of the lengths of the sides of a polygon
Linear measurement
A one dimensional measurement (length, distance)
Area
The number of square units contained in the interior of a polygon
Area of a square
Area of a square is the square of the length of its side
A= s2
Area congruence postulate
If two polygons are congruent, then they have the same area
Area addition postulate
The area of a REGION is the sum of the areas of all it’s nonoverlapping parts
Area of a rectangle thm
The area of a rectangle is the product of its base and height
A=b•h
Area of a parallelogram thm
The area of a parallelogram is the product of a base and its corresponding height, or
A= b•h
Corresponding height
Length of the altitude drawn to the chosen base
Area of a triangle thm
The area of a triangle is half the product of a base and its corresponding height, or
A=1/2(b•h)
Area of a trapezoid thm
The area of a trapezoid is half the product of the height and the sum of the bases, or
A= 1/2 h (b1 + b2)
If the diagonals of a quadrilateral are perpendicular, then
Then the area of the quadrilateral is half the product of the length of the diagonals, or
A= 1/2 (d1) (d2)
Kite
A quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent
Apothem of a regular polygon
The distances between the center and a side
Central angle of a regular polygon
Angle whose vertex is the center and whose sides contain two consecutive vertices of a polygon
Thm 11.7: area of a regular polygon
The area of a regular polygon is one half of the product of the apothem (a) and the perimeter (p)
A= 1/2 AP
Circumference
Distance around a circle
Circumference of a circle
The ratio of the circumference C and the diameter D of any circle is pi
C= 2pi r
Arc length
Fraction of the circumference of a circle
2 pi r (m
Area of a circle
A= pi r2
Actor of a circle
REGION bounded by to radii of the circle and their intercepted arc
Area of a sector
Pi r2 (m
Segment of a circle
Region of a circle bounded by a cord and is intercepted arc
Minor segment
Segment whose arc is less than 180°
Area of a minor segment
(Area of sector) - (area of triangle)
Center of a regular polygon
Center of the circle circumscribed about the polygon
Radius of a polygon
Radius of the circumscribed circle
Theorem 11.11: areas of similar polygons theorem
If two polygons are similar with corresponding sides in the ratio of a: B, then the ratio of the areas is a2 : b2
