Triangles

Triangles

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

  1. \(\color{blue}{45^{\circ}}\)
  2. \( \color{blue}{ 15^{\circ}}\)
  3. \( \color{blue}{ 40^{\circ}}\)

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