Trapezium Area Formula Explained

The area of a trapezium is calculated using a specific formula that involves the lengths of its parallel sides and its height.

Understanding the Trapezium Area Formula

• A trapezium is a quadrilateral with at least one pair of parallel sides.
• The formula requires the lengths of the two parallel sides (often denoted as a and b) and the perpendicular height (h) between these sides.
• The formula is:
  Area = \(\left(\frac{1}{2}\right) \times (\text{Sum of parallel sides}) \times \text{height}\)
• This can be written using variables as:
  Area = \(\frac{1}{2} \times (a + b) \times h\)

Identifying the Correct Formula

Comparing the standard formula with the given options:

• Option 1: \(\left(\frac{1}{4}\right) \times \text{base} \times \text{height}\) - Incorrect. This resembles the area of a triangle scaled incorrectly.
• Option 2: \(\left(\frac{1}{2}\right) \times \text{base} - \text{height}\) - Incorrect. Uses subtraction and only one base.
• Option 3: \(\left(\frac{1}{2}\right) \times (\text{Sum of parallel sides}) \times \text{height}\) - Correct. This accurately represents the area of a trapezium.
• Option 4: \(\text{Base} \times \text{height}\) - Incorrect. This is the formula for the area of a rectangle or parallelogram.

Therefore, the correct formula for the area of a trapezium is presented in Option 3.