Question

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

Answer 1

Answer: 37.947 is what i got

Answer 2

D. 37.947

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.