Shape Splitters Area Worksheet
6th Grade Math Scaffolded Geometry
Shape Splitters Area Worksheet
Decomposing shapes into unit triangles and squares to find total area
Name:
Date:
Reference Toolkit: Tangram Building Blocks
1/2-Unit Triangle Area = 0.5 sq units Half of 1 square
1-Unit Square Area = 1.0 sq unit 1 full grid box
1-Unit Triangle Area = 1.0 sq unit Half of 1x2 rectangle
2-Unit Triangle Area = 2.0 sq units Half of 2x2 square
1 Part 1: Count & Combine Tangram Pieces
Count whole squares and combine matching half-triangles
A. "The Arrowhead"
Full 1-unit squares: ____
1/2-unit triangles: ____
1-unit triangles: ____
Total Area:
B. "The Fox Head"
2-unit triangles: ____
1-unit triangles: ____
Calculation: __ + __ =
Total Area:
2 Part 2: Decompose & Tally the Tangram Bird
Identify each numbered shape piece, write its area, and sum
① ② ③ ④ ⑤ ⑥
1 grid square = 1 sq unit
| Piece | Type of Shape | Area (sq units) |
|---|
| Piece ① | 1-Unit Square | 1.0 |
| Piece ② | 1/2-Unit Triangle | 0.5 |
| Piece ③ | 2-Unit Triangle | 2.0 |
| Piece ④ | 2-Unit Triangle | 2.0 |
| Piece ⑤ | 1/2-Unit Triangle | 0.5 |
| Piece ⑥ | 1/2-Unit Triangle | 0.5 |
Sum: 1.0 + 0.5 + 2.0 + 2.0 + 0.5 + 0.5 =
Total Bird Area:
___ sq un
Pro-Tip for Area: Two 1/2-unit triangles always make 1 whole square unit! Combine pairs of half-units first to make adding easy!
Page 2 Practice
Decompose Odd Shapes into Triangles & Rectangles
1 Grid Box = 1 Square Unit (1 unit × 1 unit)
Strategy: Draw partition lines → find each area → add up!
1 The L-Shape Room 2 Rectangles
Draw a dashed line across or down to split into 2 rectangles.
A B
Piece A (Top): 1 × 2 = ____ sq units
Piece B (Bottom): 3 × 1 = ____ sq units
Total Area:
A + B =
2 The House Pentagram Square + Triangle
Split along the roofline into a triangle roof and square base.
Roof (A) Base (B)
Base Rectangle (B): 3 × 2 = ____ sq units
Roof Triangle (A): (3 × 1) ÷ 2 = ____ sq un
Total Area:
A + B =
3 The Trapezoid Stage 1 Rect + 2 Triangles
Partition the trapezoid into a center rectangle and 2 outer wings.
T1 R T2
Center Rect (R): 1 × 2 = ___ sq units
Left Tri (T1): (1 × 2) ÷ 2 = ___ sq un
Right Tri (T2): (1 × 2) ÷ 2 = ___ sq un
Total Area:
T1 + R + T2 =
4 The Arrow Flag (Your Turn!) Independent
Draw your own split lines right on the grid, then show work.
Shaft Rectangle: Area = ____ sq units
Arrowhead Triangle: Area = ____ sq units
Total Area:
Total =
Decomposition Master Checklist
I drew lines along the grid to make basic shapes.
I used formulas or counted unit boxes for each piece.
I added all piece areas together for the grand total.
How confident do you feel decomposing shapes? (Circle one):
🌱 Need Help 🌿 Getting It 🌳 Shape Master!
