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A triangle has sides with lengths: 3, 8, and 9. How do you find the area of the triangle using Heron's formula?

1 Answer

Jan 17, 2016

$A = 2 \sqrt{35}$ $A=2sqrt35$

Explanation:

First, find the triangle's semiperimeter. This is used in Heron's formula.

$s = \frac{a + b + c}{2}$ $s=(a+b+c)/2$

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

$s = \frac{3 + 8 + 9}{2} = 10$ $s=(3+8+9)/2=10$

Heron's formula, which gives the area of a triangle, is

$A = \sqrt{s (s - a) (s - b) (s - c)}$ $A=sqrt(s(s-a)(s-b)(s-c))$

$A = \sqrt{10 (10 - 3) (10 - 8) (10 - 9)}$ $A=sqrt(10(10-3)(10-8)(10-9))$

$A = \sqrt{10 \times 7 \times 2}$ $A=sqrt(10xx7xx2)$

$A = \sqrt{2^{2} \times 5 \times 7}$ $A=sqrt(2^2xx5xx7)$

$A = 2 \sqrt{35}$ $A=2sqrt35$

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