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GEOMETRY Square Area NAME_________________________ DATE __________ Per.___________ 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)