Solving the Trapezium Area Problem: A Step-by-Step Guide

Are you tackling a trapezium area problem and finding it challenging? Fear not, as we will walk through this problem together. This guide will provide a detailed solution and ensure that you understand the process. Remember, the journey to mastering such problems involves both patience and a keen understanding of the underlying principles.

Understanding the Problem

The problem you are working on involves a trapezium, which is a four-sided shape with one pair of parallel sides. The distance between these parallel sides (AB and DC) is given as 4 cm, the length of one of these sides (AB) is 8 cm, and the area of the trapezium is 26 cm2. You are asked to find the length of the other parallel side (DC).

Step-by-Step Solution

To solve this problem, we will use the formula for the area of a trapezium:

Area 1/2 x (Sum of parallel sides) x height

Let's denote the length of the other parallel side (DC) as b.

Step 1: List the Known Values

Distance between parallel sides ABC and DC: 4 cm (height) Length of side AB: 8 cm Area of trapezium: 26 cm2

Now, plug these values into the formula for the area of a trapezium to solve for b.

Step 2: Apply the Formula

Using the formula:

26 1/2 x (8 b) x 4

First, simplify inside the parentheses:

26 1/2 x (8 b) x 4

To eliminate the fraction, multiply both sides by 2:

52 (8 b) x 4

Divide both sides by 4:

13 8 b

Step 3: Solve for b

Subtract 8 from both sides:

5 b

Therefore, the length of side DC is 5 cm.

Understanding the Solution

Breaking down the problem into smaller steps makes it easier to understand and tackle. Here are some key points to remember:

Area Formula for Trapezium: The formula for the area of a trapezium is Area 1/2 x (Sum of parallel sides) x height. Step-by-Step Approach: Break down the problem into smaller, manageable steps to ensure accuracy and clarity. Check Your Work: Double-check your calculations to avoid mistakes.

Conclusion

Always remember that practice and patience are key in solving complex problems. With time and consistent effort, you will become adept at tackling even the trickiest algebraic questions. Don't hesitate to seek help from teachers, tutors, or online resources if you are struggling. The journey to mastering these concepts is rich with learning and growth.