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

- \(\color{blue}{45^{\circ}}\)
- \( \color{blue}{ 15^{\circ}}\)
- \( \color{blue}{ 40^{\circ}}\)