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In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulae for the area of a triangle, such as half the base times the height. Use Heron's Formula to find the area, in square yards, of ΔABC.

A. 7.746
B. 33.941
C. 30.984
D. 34.947

In geometry Herons formula sometimes called Heros formula named after Hero of Alexandria gives the area of a triangle by requiring no arbitrary choice of side class=

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sqdancefan

Answer:

  D.  37.947

Step-by-step explanation:

Heron's formula makes use of the value "s", the semi-perimeter. Here, ...

  s = (7 + 11 + 12)/2 = 15

Then the area is ...

  A = √(s(s -a)(s -b)(s -c)) = √(15·3·4·8) = √1440 = 12√10 ≈ 37.947

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Comment on answer choices

This value is verified by a triangle solver. We suspect a typographical error in the answer choices, specifically, selection D.

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