11.2-11.3 Areas of Parallelograms, Triangles, and Trapezoids

Rectangle

Formula: Area = Base × Height
Example Calculation: Given base = 4, height = $2\sqrt{2}$, Area = $4 \times 2\sqrt{2} = 8\sqrt{2}$ square meters.

Parallelogram

Formula: Area = Base × Height
Example Calculation: Given base = 5, height = 10, Area = $5 \times 10 = 50$ square centimeters.

Triangle

Formula: Area = (1/2) × Base × Height
Example Calculation: Given base = 12, height = 8, Area = (1/2) × 12 × 8 = 48 square inches. In instances where height isn't provided, derive it using special triangles.

Trapezoid

Formula: Area = (1/2) × Height × (Base1 + Base2). Understanding the median simplifies calculations; Median = (Base1 + Base2) / 2.

Overview

These notes summarize key formulas for calculating areas of geometric shapes, emphasizing the importance of deriving missing dimensions and practice with properties for problem-solving efficiency.