Introduction to the Trapezium and its Calculations

A trapezium (or trapezoid in some regions) is a fascinating quadrilateral characterized by two parallel sides (bases) and two non-parallel sides (legs). The area of a trapezium is calculated using the formula: Area ((base1 base2) * height) / 2. This formula is a cornerstone in geometry and is widely applied in various fields such as construction, engineering, and mathematics.

In this article, we will explore a specific problem related to the area of a trapezium: calculating the sum of its parallel sides given its area and height. Let us delve into a real-life example to enforce our understanding.

Example

Suppose the area of a trapezium is 262.5 square centimeters and its height is 15 centimeters. We need to find the sum of the parallel sides.

Given the formula for the area of a trapezium:

Area ((base1 base2) * height) / 2

Let us denote:

Area (A) 262.5 Height (h) 15 cm Sum of parallel sides (base1 base2) x cm

We want to solve for x.

Step-by-Step Solution

Step 1: Rearrange the formula to solve for the sum of the parallel sides:

x 2 * Area / height

Step 2: Substitute the given values into the formula:

x 2 * 262.5 / 15

Step 3: Calculate the value:

2 * 262.5 525

525 / 15 35

Therefore, the sum of the parallel sides (base1 base2) is:

boxed{35} cm

Alternative Solutions

Let us explore a few more ways to arrive at the same solution:

Using the Formula: area (base1 base2) * height / 2

Given:

area 262.5 height 15 cm

Solve for (base1 base2):

262.5 (base1 base2) * 15 / 2

(base1 base2) 262.5 * 2 / 15

(base1 base2) 35 cm

Let the Sum of Parallel Sides be x cm

Given:

Area 262.5 Height 15 cm Sum of parallel sides x cm

Using the formula:

262.5 (1/2) * x * 15

x (262.5 * 2) / 15

x 35 cm

Conclusion

To sum up, the sum of the parallel sides of a trapezium can be calculated by rearranging the area formula and substituting the given values. This method offers a simple and effective way to solve for missing dimensions in trapeziums, making it an invaluable skill in geometry and related fields. When tackling trapezium problems, it is essential to carefully apply the formula and ensure accurate calculations.