To calculate the **area** of a trapezoid, add the lengths of the two parallel sides (a and b), divide the result by 2, and then multiply by the height (h). This will give you the total area of the trapezoid.

## Trapezoid Area Calculator

The Trapezoid Area Calculator helps you determine the area of any trapezoid using simple inputs like base lengths and height. Whether you need to calculate the area of a regular, right, or irregular trapezoid, this tool simplifies the process. It also includes features for more complex shapes, allowing you to solve for the area even without the height. Perfect for students, engineers, and DIY projects.

**Formula:**

The formula is:

$\text{A} = \frac{a + b}{2} \times h$

Variable |
Meaning |
---|---|

A | Area (the total area of the trapezoid) |

a | Length of the first parallel side (in meters, feet, etc.) |

b | Length of the second parallel side (in meters, feet, etc.) |

h | Height (the perpendicular distance between the two parallel sides) |

**Solved Calculations :**

**Example 1:**

**Given**:

- Side a = 6 meters
- Side b = 10 meters
- Height (h) = 5 meters

Calculation |
Instructions |
---|---|

Step 1: A = $\frac{a + b}{2} \times h$ |
Start with the formula. |

Step 2: A = $\frac{6 + 10}{2} \times 5$ |
Replace a with 6, b with 10, and h with 5. |

Step 3: A = $\frac{16}{2} \times 5$ |
Add 6 and 10 together. |

Step 4: A = 8 \times 5 |
Divide 16 by 2. |

Step 5: A = 40 square meters |
Multiply by the height. |

**Answer**:

The area of the trapezoid is **40 square meters**.

**Example 2:**

**Given**:

- Side a = 4 feet
- Side b = 8 feet
- Height (h) = 6 feet

Calculation |
Instructions |
---|---|

Step 1: A = $\frac{a + b}{2} \times h$ |
Start with the formula. |

Step 2: A = $\frac{4 + 8}{2} \times 6$ |
Replace a with 4, b with 8, and h with 6. |

Step 3: A = $\frac{12}{2} \times 6$ |
Add 4 and 8 together. |

Step 4: A = 6 \times 6 |
Divide 12 by 2. |

Step 5: A = 36 square feet |
Multiply by the height. |

**Answer**:

The area of the trapezoid is **36 square feet**.'

**What is Trapezoid Area Calculator ?**

The **Trapezoid Area Calculator** is a tool that helps you quickly find the area of a trapezoid using its base lengths and height. The basic formula for calculating the area of a trapezoid is: **Area = ½ × (Base1 + Base2) × Height**.

This formula works by averaging the lengths of the two parallel sides (the bases) and multiplying that by the height of the trapezoid. If the height is not provided, you can use other methods, such as the **Pythagorean theorem** or the properties of right trapezoids to determine it.

For more complex shapes, such as irregular or **scalene trapezoids**, the area calculation may require additional measurements or specific geometric rules.

The **trapezoidal rule** is also used to approximate areas under curves, making it useful in various applications. Additionally, you can use the calculator to find the area in **square feet** or **square meters**, depending on your needs.

For cases where the height is unknown, you can still calculate the area by using side lengths and angles in specific formulas, ensuring that even tricky trapezoid shapes can be solved.