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

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

## Related Topics

- How Calculate the Area of Trapezoids
- How to Find the volume and surface area of Rectangular Prisms
- How to Find the Area and Circumference of Circles
- How to Find Volume and Surface Area of Cubes
- How to Find the Perimeter of Polygons

## 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

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

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