alvindavis99

CIP School in the Phils.

Geometry: Area Formulas

on August 23, 2012

 

 

 

triangle-rectangle-hexagon pattern (dodecagon)

triangle-rectangle-hexagon pattern (dodecagon) (Photo credit: eilonwy77)

(pi = pi = 3.141592…)

Area Formulas

 

Note: “ab” means “a” multiplied by “b”. “a2” means “a squared”, which is the same as “a” times “a”.

 

Be careful!! Units count. Use the same units for all measurements. Examples

 

square = a 2

rectangle = ab

parallelogram = bh

trapezoid = h/2 (b1 + b2)

circle = pi r 2

ellipse = pi r1 r2

 

 

 

triangle = one half times the base length times the height of the triangle

 

equilateral triangle =

 

triangle given SAS (two sides and the opposite angle)
= (1/2) a b sin C

triangle given a,b,c = sqrt[s(s-a)(s-b)(s-c)] when s = (a+b+c)/2 (Heron’s formula)

regular polygon = (1/2) n sin(360°/n) S2
   when n = # of sides and S = length from center to a corner

  Units

Area is measured in “square” units. The area of a figure is the number of squares required to cover it completely, like tiles on a floor.

Area of a square = side times side. Since each side of a square is the same, it can simply be the length of one side squared.

If a square has one side of 4 inches, the area would be 4 inches times 4 inches, or 16 square inches. (Square inches can also be written in2.)

 

Be sure to use the same units for all measurements. You cannot multiply feet times inches, it doesn’t make a square measurement.

 

The area of a rectangle is the length on the side times the width. If the width is 4 inches and the length is 6 feet, what is the area?

NOT CORRECT …. 4 times 6 = 24

CORRECT…. 4 inches is the same as 1/3 feet. Area is 1/3 feet times 6 feet = 2 square feet. (or 2 sq. ft., or 2 ft2).

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