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