Download 4. Square Area Formula from Rectangle Area: 3.

GEOMETRY
Square Area
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Areas
3. Square Area Formula from Rectangle Area:
Instead of postulating that the area of a square is s2 and deriving the area of a rectangle is bh, assume
the area of a rectangle is bh and derive the area formula for the square.
RECTANGLE AREA POSTULATE
A = bh
s
s
h
b
As a square is also a rectangle
with base b = ___, and height h
= ___,
then area A = bh =
If we postulate the formula for the area of a rectangle, what is the theorem to be proved?
If the area of the square formula is a postulate, what can be proved as a theorem?
4.
Area formulas for the square and rectangle can be used to simplify arithmetic multiplication of
large numbers without a calculator.
30
7
EXAMPLE: 23 × 37
Rewrite 23 and 20 + 3 and 37 as 30 + 7.
20
Then model this problem as
the sum of rectanglular areas.
Fill in the area of each rectangle at right:
3
So 23(37) = (20+3)(30+7) = 600 + 140 + 90 + 21 = 621 + 230 = 851. (Confirm with a calculator.)
Label the sides of each rectangle b) 56 × 89 =
and add the regions.
a) 3 × 42 =
5.
c) 77 × 154 =
Use area formulas for squares and rectangles to multiply algebraic polynomials.
Label the sides of each square and rectangle, find each area, and add the regions.
a) ( x + 3)2 = ( x + 3)( x + 3)
b) (x + 5)(x − 2)
c) (2x + 7)(x + 9)