Area of Three Triangles

Directions: Use the integers 2 through 10, at most one time each, as lengths of individual sides to form three triangles. What is the smallest total area of the three triangles you can create? What is the largest?


For Geometry: You will need to give them Heron’s formula if they don’t know it.
For Trig: “How can we find the area of a triangle if we know all three sides but no angles?”
In general: “How can I make sure all three are triangles?”


Minimum Area: 2-9-10, 3-6-7 and 4-5-8
Maximum Area: 2-3-4, 5-6-7, 8-9-10

Source: Dan Wulf

Print Friendly, PDF & Email

Check Also

Equations of Circles 1

Directions: Using the integers -9 to 9, at most one time each, fill in the …


  1. Why do you have multiple “minimum” area answers? And multiple “maximum”?

    And why was 2, 3, 4 included…

    These answers don’t make sense to me, am I missing something?

    • I am reading the answers as the measurements of the three sides. We need to find three sets of three numbers. 2, 3, 4 are valid from the question

  2. I am so confused on how to do area of a triangle? HELP

  3. It seems you would be allowed to “reuse” the length of a side for a second triangle. For example, use the length of 10 in three triangles if you allowed the triangles to overlap.

Leave a Reply

Your email address will not be published. Required fields are marked *