# 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.

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

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