How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 28, and 21 units in length?

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Answer 1 · 2015-12-29T08:36:04

$24sqrt111$ $"units"^2$

Heron's formula:

$A=sqrt(s(s-a)(s-b)(s-c))$

When $s$ , the semiperimeter, is equal to

$s=(a+b+c)/2$

when $a,b,c$ are the sides of the triangle.

Find $s$ first:

$s=(25+28+21)/2=37$

Thus,

$A=sqrt(37(37-25)(37-28)(37-21))$

$A=sqrt(37xx12xx9xx16)$

$A=sqrt37xxsqrt(2^2xx3)xxsqrt(3^2)xxsqrt(4^2)$

$A=(2xx3xx4)sqrt(37xx3)$

$A=24sqrt111~~252.8557$