Area of the Trapezium is

Question

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RRB ALP 2018 CBT 2 Fitter Question Paper (21-Jan-2019) (Shift 3)

$\left(\frac{1}{4}\right) \times \text{base} \times \text{height}$

$\left(\frac{1}{2}\right) \times \text{base} - \text{height}$

$\left(\frac{1}{2}\right) \times (\text{Sum of parallel sides}) \times \text{height}$

$\text{Base} \times \text{height}$

The correct answer is

$\left(\frac{1}{2}\right) \times (\text{Sum of parallel sides}) \times \text{height}$

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.

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 = $\frac{1}{2} \times (a + b) \times h$

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.

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