Math Example--Area and Perimeter--Quadrilaterals: Example 4

Topic

Geometry

Description

This example demonstrates the calculation of a rectangle's area using algebraic expressions. The rectangle ABCD has a length of x + 10 units and a width of x - 3 units. To find the area, we use the formula A = l × w, where l is the length and w is the width. In this case, A = (x + 10)(x - 3) = x² + 7x - 30 square units.

Incorporating algebra into geometry problems helps students connect different mathematical concepts. This collection of examples bridges the gap between basic geometry and more advanced mathematical thinking. By working with variables and expressions, students develop skills in both geometric reasoning and algebraic manipulation, preparing them for more complex mathematical challenges.

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 problem-solving skills. This approach helps students become more comfortable with abstract thinking and prepares them for more advanced mathematical concepts in higher-level courses.

Teacher Script: "Let's examine this rectangle with algebraic dimensions. Our length is x + 10 and our width is x - 3. To find the area, we multiply these together. Let's use the FOIL method: First, Outer, Inner, Last. Can you follow along as we multiply (x + 10)(x - 3)? Great! Now, let's simplify our expression. See how we end up with x² + 7x - 30? This shows us how the area changes as x changes. It's a powerful way to understand the relationship between a shape's dimensions and its area!"

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