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HISTORY OF MATH

(8) Given a quadrilateral with sides a, b, c, d the Egyptians used the following formula for the area A)0 This is not correct, so lets see what is wrong with it. Below is a quadrilateral ABCD with its two diagonals. (a) Fix the following formula: (There is only one little thing that has to be changed!) area(ABC D)-area (AABD)+ area (AACD) +area (ABCD)+area (AABC) b) Now find the area for each of the triang- les involved. For example, your area for △ABD should involve LA. a, and b (c) Use the areas you found in (b) and the corrected formula from (a) to find a cor rect formula for area (ABCD) d) Finally, multiply out the Egyptian for- mula and compare the two. When is the Egyptian formula a good approxi- mation?

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