Composite Figures Review Packet
3rd Grade Math Unit 3 Review • 3.MD.C.7b,d
Area Architects: Composite Figures
Mastering Decomposing, Multi-Part Figures & The Subtraction Strategy
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Date:
Concept 1
Decomposing into Rectangles (Additive Strategy)
A composite figure is made of two or more rectangles joined together. To find its total area: 1. Split the shape into non-overlapping rectangles (A and B). 2. Multiply (\(\text{length} \times \text{width}\)) for each part. 3. Add the partial areas together!
Memory Refresher Worked Example (Already Solved!)
Study the steps below
A B 4 cm 5 cm 10 cm 3 cm
Rectangle A: \(4\text{ cm} \times 5\text{ cm} = \mathbf{20\text{ sq cm}}\)
Rectangle B: \(10\text{ cm} \times 3\text{ cm} = \mathbf{30\text{ sq cm}}\)
Total Area = 20 + 30 = 50 square cm
Your Turn
Decompose each shape into two rectangles, find each partial area, and add.
Problem 1
3 cm 8 cm 5 cm 8 cm 3 cm
Show your decomposition line and calculations:
Rectangle A: _____ × _____ = _____ sq cm
Rectangle B: _____ × _____ = _____ sq cm
Total Area = _____ + _____ = _______ sq cm
Problem 2
5 cm 7 cm 4 cm 4 cm 9 cm
Show your decomposition line and calculations:
Rectangle A: _____ × _____ = _____ sq cm
Rectangle B: _____ × _____ = _____ sq cm
Total Area = _____ + _____ = _______ sq cm
Lesson 11 & 12 Review • Additive Decomposition Page 1 of 3
Unit 3 Review • Lesson 12
Concept 2: T-Shapes, U-Shapes & 3-Part Figures
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Core Rule
Splitting Multi-Piece & Symmetrical Figures
Figures like T-shapes and U-shapes can be broken down into 2 or 3 simple rectangles. Important Math Rule: No matter which way you decompose a figure, the total area is always the same!
Memory Refresher T-Shape Worked Example (Already Solved!)
Top Bar + Vertical Stem
Top Bar A Stem B 8 cm 2 cm 3 cm 5 cm
Top Bar (A): \(8\text{ cm} \times 2\text{ cm} = \mathbf{16\text{ sq cm}}\)
Stem (B): \(3\text{ cm} \times 5\text{ cm} = \mathbf{15\text{ sq cm}}\)
Total Area = 16 + 15 = 31 square cm
Your Turn
Find the area of each composite figure. Show your work clearly.
Problem 3 (T-Shape)
10 cm 3 cm 4 cm 4 cm
Decompose into Top Bar & Stem:
Top Bar: _____ × _____ = _____ sq cm
Stem: _____ × _____ = _____ sq cm
Total Area = _____ + _____ = _______ sq cm
Problem 4 (U-Shape / 3 Parts)
2 cm 2 cm 6 cm 4 cm 8 cm 2 cm
Split into 3 rectangles (Left Pillar, Right Pillar, Bottom Bar):
Left Pillar: ___ × ___ = ___ sq cm
Right Pillar: ___ × ___ = ___ sq cm
Bottom Bar: _____ × _____ = _____ sq cm
Total = ___ + ___ + ___ = _______ sq cm
Lesson 12 Review • Multi-Part & Stepped Figures Page 2 of 3
Unit 3 Review • Lesson 13
Concept 3: The Subtraction Strategy
Name:
The "Cut-Out" Method
Whole Rectangle Area Minus The Missing Piece
Instead of cutting a shape into pieces, imagine the full, complete rectangle first!
Step 1: Find the area of the whole rectangle (\(\text{length} \times \text{width}\)). Step 2: Find the area of the cut-out piece that is missing. Step 3: Subtract the missing piece from the whole!
Memory Refresher Subtraction Worked Example (Already Solved!)
\(\text{Area} = \text{Whole} - \text{Cut-Out}\)
Cut-out 9 ft (Whole width) 7 ft 4 ft 3 ft
Whole Rectangle: \(9\text{ ft} \times 7\text{ ft} = \mathbf{63\text{ sq ft}}\)
Cut-Out Piece: \(4\text{ ft} \times 3\text{ ft} = \mathbf{12\text{ sq ft}}\)
Area = Whole − Cut-Out 63 − 12 = 51 sq ft
Your Turn
Use the Subtraction Strategy to find the area of each figure.
Problem 5
10 cm (Whole width) 8 cm 4 cm 3 cm
Whole rectangle: _____ × _____ = _____ sq cm
Cut-out piece: _____ × _____ = _____ sq cm
Area = Whole − Cut-out _____ − _____ = _______ sq cm
Problem 6
9 in (Whole width) 8 in 4 in 3 in
Whole rectangle: _____ × _____ = _____ sq in
Cut-out piece: _____ × _____ = _____ sq in
Area = Whole − Cut-out _____ − _____ = _______ sq in
Math Talk Reflection: Adding vs. Subtracting
When would you choose to use the Subtraction Strategy instead of decomposing into pieces?
Lesson 13 Review • The Subtraction Strategy Page 3 of 3
