Math Example--Area and Perimeter--Quadrilaterals: Example 16

Topic

Geometry

Description

This example demonstrates the calculation of a rectangle's perimeter using algebraic expressions. The rectangle ABCD has a length of x + 25 units and a width of x - 7 units. To find the perimeter, we use the formula P = 2(l + w), where l is the length and w is the width. In this case, P = 2[(x + 25) + (x - 7)] = 2(2x + 18) = 4x + 36 units.

Incorporating algebra into geometry problems helps students connect different mathematical concepts and develop more advanced problem-solving skills. This collection of examples bridges the gap between basic geometry and algebraic thinking, preparing students for more complex mathematical challenges they will encounter in higher-level courses.

Multiple worked-out examples are essential for students to grasp the interplay between geometry and algebra. Each example builds upon previous knowledge while introducing new complexities, allowing students to gradually develop their analytical skills. This approach helps students become more comfortable with abstract thinking and enhances their ability to tackle real-world problems that often involve both geometric and algebraic elements.

Teacher Script: "Let's explore this rectangle with algebraic dimensions. Our length is x + 25 and our width is x - 7. To find the perimeter, we need to add all four sides. We can use the formula 2(l + w) as a shortcut. Let's substitute our expressions: 2[(x + 25) + (x - 7)]. Can you help me simplify this? Great! We end up with 4x + 36. This expression shows us how the perimeter changes as x changes. It's a powerful way to understand the relationship between a shape's dimensions and its perimeter!"

For a complete collection of math examples related to Area and Perimeter click on this link: Math Examples: Quadrilateral Area and Perimeter Collection.