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

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

## 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.

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

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