Shape Shifters Review Packet Geometry Review Unit
Shape Shifters Review Packet
Name:
Date:
Period:
Do Now
Warm-Up: Foundations of Area
Time: 5 Minutes
1. Evaluate:
\( (13 \times 9) \div 2 \)
2. Rectangle area:
Base = \(12\text{ cm}\), Height = \(7.5\text{ cm}\)
3. Concept Check:
Perimeter measures ; Area measures .
Vocabulary
Essential Geometry Terminology
Polygon: A closed, 2D flat shape formed entirely by three or more straight line segments that meet only at their endpoints and never cross.
Base & Height: The base (\(b\)) is any chosen side; height (\(h\)) is the perpendicular segment (\(90^\circ\)) connecting the base to the opposite vertex or side.
Decompose: To break apart a complicated figure into simpler, non-overlapping shapes (like rectangles, squares, and triangles).
Composite / Funky Figure: A non-standard shape created by joining two or more basic geometric polygons together.
Skill 1
Polygon or Not? (Identifying Polygons)
Test: 2D flat? Closed? Straight lines only? No crossings?
Figure A Shape #1
Is it a polygon? YES / NO
Explain why / why not:
Figure B Shape #2
Is it a polygon? YES / NO
Explain why / why not:
Figure C Shape #3
Is it a polygon? YES / NO
Explain why / why not:
Figure D Shape #4
Is it a polygon? YES / NO
Explain why / why not:
Rule to Remember: A polygon must be closed , two-dimensional (flat) , and made of straight line segments only (no curves, no 3D solids, no openings). Page 1 of 3
Core Formulas in Action
Part 2: Triangles & Parallelograms
Review Packet
Page 2
Skill 2 Area of a Parallelogram
Area = b × h
Crucial Reminder: Height must be perpendicular (\(90^\circ\)) to base. Ignore slant sides when computing area!
Problem 1 Find the Area
b = 14 cm h = 6 cm slant = 7.2 cm
Show Work:
Area =
Problem 2 Grid & Dimensions
b = 9.5 m h = 4 m
Show Work:
Area =
Skill 3 Area of a Triangle
Area = ½ × b × h
Why ½? Every triangle is exactly half of a parallelogram with the exact same base and height!
Problem 3 Acute / Right Triangle
b = 16 in h = 8 in
Show Work:
Area =
Problem 4 Obtuse Triangle (Outside Height)
b = 10 cm h = 7 cm
Show Work:
Area =
Key Check: Did you remember to divide by 2 for the triangles? Page 2 of 3
Decomposition Mastery
Part 3: Trapezoids & Funky Shapes
Review Packet
Page 3
The Decomposition Protocol: 1. Draw dashed cut lines; 2. Find missing dimensions; 3. Calculate sub-areas; 4. Add them up!
Skill 4
Trapezoids Decomposed into Rectangles & Triangles
Problem 5: Right Trapezoid
top = 8 cm 6 cm total bottom = 14 cm Rectangle Triangle
Area Rect:
Area Tri:
Total Area =
Problem 6: Symmetrical Trapezoid
top = 8 m h = 5 m bottom = 16 m Tri 1 Tri 2
Rect:
2 Triangles:
Total Area =
Skill 5
Funky Shapes (Compound / Composite Figures)
Problem 7: Composite House Shape
base = 10 ft 4.5 ft roof h = 4 ft
Decompose & Compute:
Total Area =
Problem 8: Funky Yard Shape
8 m 4 m 3 m total = 14 m 3 m
Decompose & Compute:
Total Area =
Review Checkpoint Complete! Keep this packet for reference during tonight's homework and tomorrow's quiz.
Page 3 of 3
Shape Shifters Exit Ticket Exit Ticket
Geometry Checkpoint • Shape Shifters
Name:
Period:
1. Classify 2 pts
Identify this polygon and state its side count:
Number of sides:
Polygon name:
Regular or Irregular?
2. Parallelogram 3 pts
Find the area. Watch out for distractors!
b = 11 m h = 5 m slant = 6 m
Show calculation:
Area = \(\text{m}^2\)
3. Decompose 4 pts
Split into a rectangle & triangle, then find total area:
7 cm 4 cm total bottom = 12 cm
Rect =
Tri =
Total = \(\text{cm}^2\)
Confidence: 1 (Need Help) 2 3 4 5 (Ready for Quiz!)
Score: ____ / 9
Cut along line for 2 student copies
Exit Ticket
Geometry Checkpoint • Shape Shifters
Name:
Period:
1. Classify 2 pts
Identify this polygon and state its side count:
Number of sides:
Polygon name:
Regular or Irregular?
2. Parallelogram 3 pts
Find the area. Watch out for distractors!
b = 11 m h = 5 m slant = 6 m
Show calculation:
Area = \(\text{m}^2\)
3. Decompose 4 pts
Split into a rectangle & triangle, then find total area:
7 cm 4 cm total bottom = 12 cm
Rect =
Tri =
Total = \(\text{cm}^2\)
Confidence: 1 (Need Help) 2 3 4 5 (Ready for Quiz!)
Score: ____ / 9
Shape Shifters Homework Worksheet Independent Practice
Shape Shifters Homework
Name:
Date:
Period:
Part 1
Polygon or Not? (Circle YES or NO and justify)
8 Points (2 pts each)
Figure 1 2 pts
Polygon? YES / NO
Why:
Figure 2 2 pts
Polygon? YES / NO
Why:
Figure 3 2 pts
Polygon? YES / NO
Why:
Figure 4 2 pts
Polygon? YES / NO
Why:
Part 2
Core Area Practice (One of Each Shape)
16 Points (4 pts each)
1. Parallelogram Area = b × h
Identify perpendicular height (watch out for slant side):
b = 14 cm h = 6.5 cm slant = 8 cm
Show calculation:
Area = \(\text{cm}^2\)
2. Triangle Area = ½ × b × h
Remember to divide base × height by 2:
b = 16 ft h = 9 ft
Show calculation:
Area = \(\text{ft}^2\)
3. Trapezoid (Decompose) Rect + Triangle
Break into 1 rectangle and 1 triangle:
top = 9 cm 8 cm total bottom = 15 cm
Rect Area:
Tri Area:
Total Area = \(\text{cm}^2\)
4. Funky Shape (Composite) Decompose & Sum
Break into simple shapes, then add areas:
6 m 9 m total base = 14 m 4 m
Part A Area:
Part B Area:
Total Area = \(\text{m}^2\)
Total: 24 Points • Show all decomposition and calculation work Shape Shifters Homework
Shape Shifters Geometry Quiz Assessment Unit 6 Geometry
Shape Shifters Geometry Quiz
Name:
Date:
Score: / 50
Section 1
Polygon or Not? (10 Points)
Circle YES or NO and justify (2.5 pts each)
Figure 1 2.5 pts
Polygon? YES / NO
Why:
Figure 2 2.5 pts
Polygon? YES / NO
Why:
Figure 3 2.5 pts
Polygon? YES / NO
Why:
Figure 4 2.5 pts
Polygon? YES / NO
Why:
Section 2
Triangles & Parallelograms (16 Points — 4 pts each)
Show formula and all calculation steps
5. Parallelogram A 4 pts
b = 16 cm h = 6.5 cm 8 cm
Show work:
Area = \(\text{cm}^2\)
6. Parallelogram B 4 pts
b = 12 in h = 7.5 in 9.2 in
Show work:
Area = \(\text{in}^2\)
7. Right Triangle 4 pts
b = 14 m 9 m 16.6 m
Show work:
Area = \(\text{m}^2\)
8. Obtuse Triangle 4 pts
b = 11 in h = 8 in
Show work:
Area = \(\text{in}^2\)
Continue to Page 2 for Trapezoid & Funky Shape Decomposition ➔ Quiz • Page 1 of 2
Shape Shifters Assessment
Section 3 & 4: Decomposition Mastery
Quiz Page 2 of 2
24 Points Total
Section 3: Trapezoids by Decomposition (12 Points — 6 pts each) Deconstruct into Triangles & Rectangles
9. Right Trapezoid 6 pts
Split into 1 rectangle and 1 right triangle:
top = 9 cm 8 cm total bottom = 15 cm
Rectangle Area:
Triangle Area:
Total Area = \(\text{cm}^2\)
10. Symmetrical Trapezoid 6 pts
Split into 1 rectangle and 2 congruent triangles:
top = 10 ft h = 7 ft total bottom = 18 ft
Rectangle Area:
2 Triangles Area:
Total Area = \(\text{ft}^2\)
Section 4: Funky Shapes / Composite Figures (12 Points — 6 pts each) Deconstruct, Calculate Sub-areas & Sum
11. Warehouse Profile 6 pts
width = 12 m 5 m roof h = 4 m
Rectangle Area:
Roof Triangle:
Total Area = \(\text{m}^2\)
12. The "Funky Flag" 6 pts
8 yd 3 yd 5 yd total base = 15 yd 5 yd
Top Strip Area:
Shape Shifters Quiz Key Teacher Key Scoring Guide & Solutions
Shape Shifters Quiz Answer Key
Total: 50 Points
Classroom Assessment
Section 1: Polygon or Not? (10 Points) 1 pt for YES/NO; 1.5 pts for written reason (2.5 pts each)
Figure 1 2.5 pts
Regular Hexagon
Polygon? YES (1 pt)
Reason: Closed 2D flat shape with straight line segments only. (1.5 pts)
Figure 2 2.5 pts
Circle
Polygon? NO (1 pt)
Reason: Has a curved boundary; polygons must have straight segments. (1.5 pts)
Figure 3 2.5 pts
Open Polyline
Polygon? NO (1 pt)
Reason: Open shape with gap; polygons must be closed. (1.5 pts)
Figure 4 2.5 pts
Irregular Arrowhead
Polygon? YES (1 pt)
Reason: Closed 2D shape with straight line segments only. (1.5 pts)
Section 2: Triangles & Parallelograms (16 Points — 4 pts each) 1 pt formula, 1.5 pts substitution, 1.5 pts answer & units
5. Parallelogram A Solution 4 pts
Base = 16 cm, Perpendicular Height = 6.5 cm. (Slant 8 cm ignored!)
Formula: \(A = b \times h\) (1 pt)
Calculation: \(16 \times 6.5 = 104\) (1.5 pts)
Area = 104 cm² (1.5 pts)
6. Parallelogram B Solution 4 pts
Base = 12 in, Perpendicular Height = 7.5 in. (Slant 9.2 in ignored!)
Formula: \(A = b \times h\) (1 pt)
Calculation: \(12 \times 7.5 = 90\) (1.5 pts)
Area = 90 in² (1.5 pts)
7. Right Triangle Solution 4 pts
Base = 14 m, Height = 9 m. (Hypotenuse 16.6 m ignored!)
Formula: \(A = \frac{1}{2} b h\) (1 pt)
Calculation: \(\frac{1}{2} \times 14 \times 9 = 7 \times 9 = 63\) (1.5 pts)
Area = 63 m² (1.5 pts)
8. Obtuse Triangle Solution 4 pts
Base = 11 in, Exterior Altitude = 8 in.
Formula: \(A = \frac{1}{2} b h\) (1 pt)
Calculation: \(\frac{1}{2} \times 11 \times 8 = 11 \times 4 = 44\) (1.5 pts)
Area = 44 in² (1.5 pts)
Shape Shifters Geometry • Teacher Assessment Key Key Page 1 of 2
Scoring Guide & Solutions
Sections 3 & 4: Decomposition Solutions
Key Page 2 of 2
24 Points Total
Section 3: Trapezoid Decomposition (12 Points — 6 pts each) Rubric: 2 pts decomposition/setup, 2 pts sub-areas, 2 pts total area & units
