How to Find the Centroid of a Triangle
Determining a Triangle's Area from Its Base and Height
Applying the Pythagorean Theorem

Determining a Triangle's Area from Its Three Sides

When you know the length of a triangle’s three sides and you don’t know an altitude, you can use Hero’s formula to find the area. Check it out:

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where a, b, and c are the lengths of the triangle’s sides and S is the triangle’s semiperimeter

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Now use Hero’s formula to calculate the area of a triangle with sides of length 5, 6, and 7. First, you need the triangle’s perimeter (the sum of the lengths of its sides), and from that you get the semiperimeter. The perimeter is 5 + 6 + 7 = 18, so you get 9 for the semiperimeter. Now just plug 9, 5, 6, and 7 into the formula:

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Identifying Triangles by Their Angles
Identifying the 30 – 60 – 90 Degree Triangle
Identifying the 45 – 45 – 90 Degree Triangle
Finding the Altitude of a Triangle
How to Find the Incenter, Circumcenter, and Orthocenter of a Triangle
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