TEACHING DEMONSTRATION

Clever Area of Trapezoid

Equal Area Substitution

🍫 Warm-Up: The Twin Chocolate Bar

🖐️ Live Hand-Signal Poll

Suppose we slide the two identical twin chocolate bars so they overlap in the middle:

We cut away the Shared Bite (②).
Alex eats the Orange Leftover (①). Bob eats the Blue Leftover (③)!

Who gets more chocolate?

1 Finger Alex gets more
2 Fingers Bob gets more
Cross Arms (=) Exactly Equal!

                  🌟 The Golden Principle:
                
                  Same Whole − Same Overlap = Same Leftover!
                
                  Orange Leftover ① = Blue Leftover ③

📐 Calculating Area of a Trapezoid

🧰 Key Dimensions

Parallel Bases Top Base (a) and Bottom Base (b) never intersect

Perpendicular Height Height (h) is the straight 90° distance between the bases

                Trapezoid Area Formula
              
                Area = 
                
                  (Top Base + Bottom Base) × Height
                  2
                
                = 
                
                  (a + b) × h
                  2
                
                💡 Why divide by 2? Two identical trapezoids join together to form a rectangle of width (a + b) and height h! So one trapezoid is exactly half.

🔍 The Mystery Problem & Spotting the Trap

📋 Problem Statement

The figure is made up of two identical right trapezoids, which are overlapping with each other.

Find the area of the shaded part.

⚠️ Trap Alert!

The grey shaded part has 6 sides!
It is a crooked L-shape, NOT a standard trapezoid or rectangle.

❌ We do NOT know its top length!
❌ We do NOT know its slanted edges!
👉 Trying to calculate it directly is a trap!

✨ Step 1: The "Aha!" Swap (Equal Area Substitution)

🏠 The 3 Rooms in Our House:

Room ① Target Shaded Room ② Shared Overlap Room ③ Friendly Trapezoid

Upper Trapezoid = Room ① + Room ②

Lower Trapezoid = Room ③ + Room ②

                Since Upper Twin = Lower Twin:
              
                ① + ② = ③ + ②
              
                🎉 Shaded Area ① = Blue Trapezoid ③!

📏 Step 2 & 3: Measure Blue Trapezoid ③ & Solve!

✍️ Workspace: Trapezoid Area Calculation

Formula: Area = (Top Base + Bottom Base) × Height ÷ 2

Area = (15 + 20) × 8 2 = 35 × 4 = 140

💡 Trick: Divide 8 ÷ 2 = 4 first! Then double 35 to 70, and double 70 to 140!

⚡ Challenge: Master the Twin!

Step 1: Equal Area Swap

Shaded Area ① = Bottom Trapezoid ③

Step 2: Hidden Top Base

Inside Top Base = 12 − 4 = 8

                  Step 3: Rapid Mental Math
                
                  Area = 
                  
                    (8 + 12) × 6
                    2
                  
                  = 20 × 3 = 60

🏆 Master of Equal Area Substitution

1

Spot the Twins

Whenever two identical shapes overlap, their total areas are always 100% equal (Upper = Lower).

2

Subtract Shared Overlap

① + ② = ③ + ② ⟹ ① = ③.
Trade the weird 6-sided L-shape for the friendly bottom right trapezoid!

3

Hunt Shifting Lengths

Subtract the overhang to uncover hidden inner bases:
20 − 5 = 15!

              🚀 Thanks for watching ;)
            
              Ready for Post-Demo Q&A.