Area of a Rectangle with Algebraic Sides: A GCSE Challenge

Calculating the area of a rectangle is a fundamental concept, but it can become more challenging when the side lengths are expressed algebraically. Let’s explore a typical GCSE problem involving finding the area of a rectangle in square meters, given the side lengths in centimeters. If you are struggling with problems like this, it might be time to seek GCSE Online Maths Tutoring to help you improve.

The Problem:

Find the area of the rectangle below. You must give your answer in m^2

Understanding the Problem: Equating Sides and Area Calculation

Since it’s a rectangle, opposite sides are equal. This allows us to form equations to solve for x and y. Once we have x and y, we can find the lengths of the sides in centimeters, convert them to meters, and then calculate the area in square meters.

Step-by-Step Solution:

Equate Opposite Sides:

Equation 1: x + 2 = 2x - 1

Equation 2: 2y = 3y - 1

Solve for x: From Equation 1:

2y = 3y - 1

1 = y

Calculate the Side Lengths in Centimeters:

Length 1: x + 2 = 3 + 2 = 5 \text{ cm}

Length 2: 2y = 2(1) = 2 \text{ cm}

Convert Centimeters to Meters:

Length 1:  5 \text{ cm} = 5/100 \text{ m} = 0.05 \text{ m}

Length 2: 2 \text{ cm} = 2/100 \text{ m} = 0.02 \text{ m}

Calculate the Area in Square Meters:

Area = Length 1 × Length 2

Area = 0.05 \text{ m} \times 0.02 \text{ m} = 0.001 \text{ m}^2

Answer:

The area of the rectangle is 0.001 \text{ m}^2.

Key Takeaways:

• Properties of Rectangles: Opposite sides are equal.
• Solving Algebraic Equations: Use your algebra skills to solve for the unknowns.
• Unit Conversions: Pay attention to units and convert them to the required units.
• Area Calculation: Remember the formula for the area of a rectangle (length × width).

These types of problems combine geometry, algebra, and unit conversion skills.