Polygon Area Guided Notes
Math Guided Notes • Grade 6
Area of Parallelograms
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Big Idea
A parallelogram is just a tilted rectangle!
Count the grid squares! If you cut the triangle off the left side and slide it to the right, it turns into a rectangle with the exact same base and height.
Cut Base = 5 sq h = 4 sq
The Formula
Area = base × height
\( A = b \times h \)
Watch Out! (Rule)
- • Base (\(b\)): Count the flat bottom grid units.
- • Height (\(h\)): Straight up-and-down units.
- • NEVER use the slanted side for height!
Model Problem (Guided Example) Count the grid squares!
5 cm slant h = 4 cm base = 8 cm
Step 1: Count base along bottom = 8 cm.
Step 2: Count straight height = 4 cm.
Step 3: Ignore the 5 cm slant side!
Step 4: Multiply: \( 8 \times 4 = \mathbf{32} \text{ cm}^2 \).
Your Turn: Use the Grid to Find the Area
Problem 1 1 square = 1 cm
h = 3 base = 7
Base (\(b\)) = ________ Height (\(h\)) = ________
Show Work: Multiply base × height
Area = ________________ cm²
Problem 2 1 square = 1 cm
h = 4 base = 6 slant: 5 cm
Base (\(b\)) = ________ Height (\(h\)) = ________
Show Work: Multiply base × height
Area = ________________ cm²
Page 1 • Parallelograms: Area = base × height
Math Guided Notes • Grade 6
Area of Triangles
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Big Idea
Every triangle is exactly HALF of a rectangle!
Look at the grid below. The rectangle has 24 total squares. The triangle cuts right through it, taking exactly 12 squares. That is why we divide by 2!
Rect = 24 sq Triangle = 12 sq
The Formula
Area = (base × height) ÷ 2
\( A = \frac{b \times h}{2} \)
3 Simple Steps
- 1. Count the flat base and straight height.
- 2. Multiply: base × height.
- 3. Cut in half: divide the answer by 2!
Model Problem (Guided Example) Count the grid squares!
h = 4 cm base = 8 cm
Step 1: Base = 8 cm, Height = 4 cm.
Step 2: Multiply: \( 8 \times 4 = 32 \).
Step 3: Divide by 2: \( 32 \div 2 = \mathbf{16} \text{ cm}^2 \).
Your Turn: Use the Grid to Find the Triangle Area
Problem 1 (Right Triangle) 1 sq = 1 cm
h = 4 base = 6
Base = ________ Height = ________
1. Multiply: ______ × ______ = ______
2. Cut in Half: ______ ÷ 2 = ______
Area = ________________ cm²
Problem 2 (Acute Triangle) 1 sq = 1 cm
h = 3 base = 8
Base = ________ Height = ________
1. Multiply: ______ × ______ = ______
2. Cut in Half: ______ ÷ 2 = ______
Area = ________________ cm²
Page 2 • Triangles: Area = (base × height) ÷ 2
Math Guided Notes • Grade 6
Area of Other Polygons
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Strategy
Split & Add: Decomposing Shapes on a Grid
When a polygon has an unusual shape, draw a line on the grid to chop it into shapes you already know: rectangles and triangles. Then find each area and add them!
Step 1
✂️ SPLIT
Chop into Shape A and Shape B.
Step 2
📐 FIND AREAS
Calculate Area A and Area B.
Step 3
➕ ADD THEM
Add both areas for the Total Area!
Model Problem: Trapezoid 1 grid square = 1 cm
Rect A Tri B 5 cm 4 3 cm
Shape A (Rectangle): \( 5 \times 4 = \mathbf{20} \text{ cm}^2 \)
Shape B (Triangle): \( (3 \times 4) \div 2 = 12 \div 2 = \mathbf{6} \text{ cm}^2 \)
Total Area: \( 20 + 6 = \mathbf{26} \text{ cm}^2 \)
Your Turn: Split on the Grid, Find Areas, and Add!
Problem 1: L-Shape 1 sq = 1 cm
A B 5 3 4 2
Area A (Tall Rect): \( 3 \times 5 = \) ________
Area B (Wide Rect): \( 4 \times 2 = \) ________
Total Area: ______ + ______ = ________ cm²
Problem 2: House Shape 1 sq = 1 cm
A (Sq) B 4 cm 4 cm h = 2 cm
Area A (Square): \( 4 \times 4 = \) ________
Area B (Roof Tri): \( (4 \times 2) \div 2 = \) ________
Total Area: ______ + ______ = ________ cm²
Page 3 • Complex Polygons: Split into Rectangles and Triangles, Then Add
