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Asked by Harley

# How do you find the area of a triangle with surds as lengths?

You find the area as usual, by using one of the formulas you already know. The only trick here is to use the lengths in square root format and not as decimal approximations until the end of calculations, as this will give you the most accurate result. Sometimes you may also notice that the surds may simplify to an exact number. For example if your base is sqrt(2) units and your height is sqrt(8) units, you’ll find the area by base times height divided by 2, and you’ll get sqrt(16)/2 or 4/2 or simply 2 square units. Notice therefore that leaving the square root intact and not using an approximated decimal gives you a very accurate and exact answer. This rule applies in general in mathematics: decimals are usually not useful within calculations so prefer exact numbers, square roots or fractions, and approximate to decimal form after calculations are done.  Fotios Tsitsos
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