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Postulates and Theorems 93

11.2 Area of a Parallelogram The area of aparallelogram is the product of a base and itscorresponding height. A5 bh (p. 721)

11.3 Area of a Triangle The area of a triangle isone half the product of a base and its

corresponding height. A5 1}2bh (p. 721)

11.4 Area of a Trapezoid The area of a trapezoidis one half the product of the height and thesum of the lengths of the bases.

A51}

2h(b1 1 b2) (p. 730)

11.5 Area of a Rhombus The area of a rhombusis one half the product of the lengths of its

diagonals.A5 1}2d1d2 (p. 731)

11.6 Area of a Kite The area of a kite is one halfthe product of the lengths of its diagonals.

A51}

2d1d2 (p. 731)

11.7 Areas of Similar Polygons If two polygonsare similar with the lengths of correspondingsides in the ratio ofa : b, then the ratio oftheir areas is a2 : b2. (p. 737)

11.8 Circumference of a Circle ThecircumferenceCof a circle is C5 dorC5 2r, where dis the diameter of the circleand ris the radius of the circle. (p. 746)

Arc Length Corollary In a circle, the ratio of thelength of a given arc to the circumference is equalto the ratio of the measure of the arc to 3608.

Arc length ofCAB

}}

2pr 5mCAB

}

3608 , or

Arc length ofCAB5mCAB}

3608p 2r(p. 747)

11.9 Area of a Circle The area of a circle is timesthe square of the radius. A5 r2 (p. 755)

11.10 Area of a Sector The ratio of the area A of asector of a circle to the area of the wholecircle (r2) is equal to the ratio of themeasure of the intercepted arc to 3608.

A}

pr25

mCAB}

3608, or A5 m

CAB}

3608p r

2(p. 756)

11.11 Area of a Regular Polygon The area of aregular n-gon with side length sis half theproduct of the apothem a and the perimeter

P, so A51}2aP, or A51}

2a p ns. (p. 763)

12.1 Eulers Theorem The number of faces (F),vertices (V), and edges (E) of a polyhedronare related by the formula F1 V5 E1 2.(p. 795)

12.2 Surface Area of a Right Prism The surfacearea Sof a right prism is S5 2B1 Ph5 aP1Ph, where a is the apothem of the base,Bisthe area of a base, Pis the perimeter of abase, and h is the height. (p. 804)

12.3 Surface Area of a Right Cylinder Thesurface area Sof a right cylinder is S5 2B1Ch5

2r

21

2rh

, whereB

is the area of abase,Cis the circumference of a base, ris theradius of a base, and h is the height. (p. 805)

12.4 Surface Area of a Regular Pyramid Thesurface area Sof a regular pyramid is

S5 B11}

2Pl, where Bis the area of the base,

Pis the perimeter of the base, and l is theslant height. (p. 811)

12.5 Surface Area of a Right Cone The surface

area Sof a right cone is S5 B11}2Cl 5 r

21

rl, where Bis the area of the base, Cis the

circumference of the base, ris the radius ofthe base, and l is the slant height. (p. 812)

12.6 Volume of a Prism The volume Vof a prismis V5 Bh, where Bis the area of a base andh is the height. (p. 820)

12.7 Volume of a Cylinder The volume Vof acylinder is V5 Bh5 r2h, where Bis the areaof a base, h is the height, and ris the radiusof a base. (p. 820)

12.8 Cavalieris Principle If two solids have thesame height and the same cross-sectionalarea at every level, then they have the samevolume. (p. 821)

12.9 Volume of a Pyramid The volume Vof a

pyramid is V51}3Bh, where Bis the area of

the base and h is the height. (p. 829)

12.10 Volume of a Cone The volume Vof a cone is

V51}

3Bh5

1}

3r

2h, where Bis the area of the

base, h is the height, and ris the radius of thebase. (p. 829)

12.11 Surface Area of a Sphere The surface area S

of a sphere with radiusr

isS5

4r

2

. (p. 838)12.12 Volume of a Sphere The volume Vof a

sphere with radius ris V5 4}3

r3. (p. 840)

12.13 Similar Solids Theorem If two similar solidshave a scale factor ofa :b, then correspondingareas have a ratio ofa2 : b2, and correspondingvolumes have a ratio ofa3 :b3. (p. 848)