How to Solve Triangles Problems? (+FREE Worksheet!)

Learn how to solve mathematics problems related to triangle area and angles using common triangle formulas.

How to Solve Triangles Problems? (+FREE Worksheet!)

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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 \(= \color{blue}{\frac{1}{2 }(base \ × \ height)}\)

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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

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

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