Triangle xy area
In this handbook, you will find a collection of problem-solving examples related to calculating the area of triangles. These examples will guide you through various scenarios and help you enhance your understanding of the concepts involved. Whether you are a student learning about geometry or someone looking to refresh their math skills, this resource can be a valuable tool in mastering triangle area calculations. The clear explanations and detailed solutions provided in this handbook aim to assist learners in improving their problem-solving skills and achieving success in tackling geometry challenges.
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Presentation Transcript
Triangle xy area Problem Solvers Handbook Ex 3.5 Q7
You are given the values of ? and ? . What s the area of the triangle? ? (not to scale) ? (The circle is tangent to the three sides of the triangle.)
? ? ? ?
? ? ? ? ? ? ? (Pythagoras) ? + ?2+ ? + ?2= ? + ?2 ?2+ 2?? + ?2+ ?2+ 2?? + ?2= ?2+ 2?? + ?2 2?2+ 2? ? + ? = 2?? ?2+ ? ? + ? = ??
? ? ? ? ? ? ?
? ? ? ? ? ? ? ????= ?2+ ?? + ?? (square and two kites) = ?2+ ? ? + ? But (found previously) ?2+ ? ? + ? = ?? ????= ?? So
Supplementary: What is the radius of the circle touching the three sides of the triangle? ? 3 4
Supplementary: What is the radius of the circle touching the three sides of the triangle? 1 23 4 = ?2+ ? 3 ? + ? 4 ? 6 = ?2+ 3? ?2+ 4? ?2 6 = 7? ?2 ?2 7? + 6 = 0 3 ? ? 1 ? 6 = 0 ? 3 So or ? = 1 ? = 6 ? 4 4 ? ?
Supplementary: What is the radius of the circle touching the three sides of the triangle? 1 23 4 = ?2+ ? 3 ? + ? 4 ? 6 = ?2+ 3? ?2+ 4? ?2 6 = 7? ?2 ?2 7? + 6 = 0 3 ? 2 ? 1 ? 6 = 0 ? 1 So or ? = 1 ? = 6 1 ? 3 4 ? 1 ? But what about the other answer?
6 6 6 1 But why did algebra bring up this answer?
? = 1 3 4 ? = 6 3 4
Whats the area of the triangle? 2 (not to scale) 4 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 3 (not to scale) 5 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 6 (not to scale) 8 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 3 (not to scale) 6 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 2 (not to scale) 5 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 3 (not to scale) 7 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 6 (not to scale) 10 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 3 (not to scale) 8 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 2 (not to scale) 3 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 4 (not to scale) 6 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 6 (not to scale) 9 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 8 (not to scale) 12 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 5 (not to scale) 7 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 6 (not to scale) 7 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 2 (not to scale) 7 (The circle is tangent to the three sides of the triangle.) SIC_11
Whats the area of the triangle? 7 (not to scale) 9 (The circle is tangent to the three sides of the triangle.) SIC_11
