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How do you find the area of a triangle when given only the lengths of three sides?

Sagot :

mathstudent55

Answer:

Use Heron's formula; see below.

Step-by-step explanation:

Use Heron's formula.

Let the sides of the triangle have lengths a, b, and c.

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

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

Example:

A triangle has side lengths 3, 4, and 5 units.

Find the area of the triangle.

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

[tex] s = \dfrac{3 + 4 + 5}{2} [/tex]

[tex] s = 6 [/tex]

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

[tex] area = \sqrt{6(6 - 3)(6 - 4)(6 - 5)} [/tex]

[tex] area = \sqrt{6(3)(2)(1)} [/tex]

[tex] area = \sqrt{36} [/tex]

[tex] area = 6 [/tex]

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