How to Solve Triangles Problems? (+FREE Worksheet!)
Learn how to solve mathematics problems related to triangle area and angles using common triangle formulas.
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A step-by-step guide to solving Triangles
- In any triangle, the sum of all angles is \(180\) degrees.
- Area of a triangle \(= \color{blue}{\frac{1}{2 }(base \ × \ height)}\)
For education statistics and research National Center for Education Statistics.
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Triangles – Example 1:
What is the area of the following triangle?
Solution:
Use the area formula: Area \(= \color{blue}{\frac{1}{2 }(base \ × \ height)}\)
base \(=10\) and height \(=6\)
Area \(= \frac{1}{2} (10×6)=\frac{1}{2} (60)=30\)
Triangles – Example 2:
What is the missing angle of the following triangle?
Solution:
All angles in a triangle sum up to \(180\) degrees. Then:: \(45+60+x=180 → 105+x=180 → x=180-105=75\)
Triangles – Example 3:
What is the area of the following triangle?
Solution:
Use the area formula: Area \(= \color{blue}{\frac{1}{2 }(base \ × \ height)}\)
base \(=12\) and height \(=8\)
Area \(= \frac{1}{2} (12×8)= \frac{1}{2} (96)=48 \)
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Triangles – Example 4:
What is the area of a triangle with base \(6\) and height \(5\)?
Solution:
Use the area formula: Area \(= \color{blue}{\frac{1}{2 }(base \ × \ height)}\)
base \(=6\) and height \(=5\)
Area \(= \frac{1}{2 } (5×6)= \frac{1}{2} (30)=15 \)
Exercises for Solving Triangles
Find the measure of the unknown angle in each triangle.
Download Triangles Worksheet
- \(\color{blue}{45^{\circ}}\)
- \( \color{blue}{ 15^{\circ}}\)
- \( \color{blue}{ 40^{\circ}}\)
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