1. As indicated earlier, Egyptian geometers used the formula A = (1)/(4)(a+c)(b+d) to calculate

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In this question, we have been given an isosceles trapezoid. Suppose this is the trapezoid that

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1. As indicated earlier, Egyptian geometers used the formula $A = \frac{1}{4}(a+c)(b+d)$ to calculate the area of any quadrilateral whose successive sides have lengths a, b, c, and d. (ii) If you choose specific lengths for the sides of an isosceles trapezoid, how does the result compare to the actual area? Repeat for two other isosceles trapezoids. Do the same for three specific parallelograms. (iii) Generalize your results for part (ii). 2. If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, Babylonian geometers approximated the length of the hypotenuse by the formula $c = b + \frac{a^2}{2b}$ (ii) Give an algebraic argument demonstrating that this formula results in an approximation that is too large.

          1. As indicated earlier, Egyptian geometers used the formula $A = \frac{1}{4}(a+c)(b+d)$ to calculate the area of any quadrilateral whose successive sides have lengths a, b, c, and d.
(ii) If you choose specific lengths for the sides of an isosceles trapezoid, how does the result compare to the actual area? Repeat for two other isosceles trapezoids. Do the same for three specific parallelograms.
(iii) Generalize your results for part (ii).
2. If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, Babylonian geometers approximated the length of the hypotenuse by the formula $c = b + \frac{a^2}{2b}$
(ii) Give an algebraic argument demonstrating that this formula results in an approximation that is too large.

1. As indicated earlier, Egyptian geometers used the formula A = (1)/(4)(a+c)(b+d) to calculate the area of any quadrilateral whose successive sides have lengths a, b, c, and d.
(ii) If you choose specific lengths for the sides of an isosceles trapezoid, how does the result compare to the actual area? Repeat for two other isosceles trapezoids. Do the same for three specific parallelograms.
(iii) Generalize your results for part (ii).
2. If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, Babylonian geometers approximated the length of the hypotenuse by the formula c = b + (a^2)/(2b)
(ii) Give an algebraic argument demonstrating that this formula results in an approximation that is too large.

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