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Type: Open-Ended
Category: Triangles
Level: Grade 11
Author: nsharp1
Created: 4 years ago

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Triangles Question

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For ΔABC, as seen below, let the intersection of the altitude from vertex B and side ¯AC be point D (not labeled). Also, let b=AC, c=AB, a=BC, x=AD, y=CD, and h=BD. Finally, let P=a+b+c and s=P2.


The area of this triangle can be expressed using Heron's formula, AΔABC=√s(s-a)(s-b)(s-c), where s=a+b+c2. The following questions will derive this formula.

Acute Triangle Height v2

Grade 11 Triangles

The form of the numerator found in the previous question should look like =(b+c+a)(b+c-a)(a+b-c)(a-b+c). Again referring to what Heron's formula should look like, the equation should have semi-perimeter variables, s. The first step will be to find the value P in the equation. Use the property z+(-z)=0 to "find" the variable P in the equation. Four P variables should be "found".