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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. 5.591
B. 7.385
C. 8.270
D. 6.495

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 a class=

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Answer:

D. 6.495 ft²

Step-by-step explanation:

s = [tex]\frac{a+b+c}{2}[/tex]        Substitute

s = [tex]\frac{7+3+5 }{2}[/tex]        Add

s = 15/2          Divide

s = 7.5

Now use the equation for area

[tex]A = \sqrt{s(s-a)(s-b)(s-c)}[/tex]       Substitute

[tex]A=\sqrt{7.5(7.5 - 7)(7.5-3)(7.5-5)[/tex]   Subtract in the parentheses

[tex]A=\sqrt{7.5(0.5)(4.5)(2.5)}[/tex]                      Multiply

[tex]A=\sqrt{42.1875}[/tex]                                     Take the square root

A = 6.495 ft²

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