Shape Splitters Area Worksheet
Practice Sheet
Area of Composite Shapes
Name:
Date:
Directions: Break each figure into three rectangles (A, B, and C). Find the area of each rectangle, then add them to find the total area.
1 U-Channel Figure
Units: centimeters (cm)
6 cm 2 cm 2 cm 9 cm 3 cm
Rectangle A:
× = sq cm
Rectangle B:
× = sq cm
Rectangle C:
× = sq cm
Total Area:
2 Stepped Podium Figure
Units: meters (m)
4 m 8 m 5 m 3 m 3 m 3 m 9 m
Rectangle A:
× = sq m
Rectangle B:
× = sq m
Rectangle C:
× = sq m
Total Area:
Page 1 of 2 • Turn over for Problems 3 & 4
Practice Sheet
Area of Composite Shapes
Name:
Page 2 of 2
Directions: Find missing side lengths, split into three non-overlapping rectangles (A, B, and C), and calculate total area.
3 Bridge Archway Figure
Units: feet (ft)
10 ft 7 ft 3 ft 3 ft 4 ft
Rectangle A:
× = sq ft
Rectangle B:
× = sq ft
Rectangle C:
× = sq ft
Total Area:
4 Asymmetrical Notch Figure
Units: yards (yd)
8 yd 3 yd 3 yd 6 yd 3 yd 11 yd
Rectangle A:
× = sq yd
Rectangle B:
× = sq yd
Rectangle C:
× = sq yd
Total Area:
End of Worksheet • Total Problems Completed: 4
Shape Splitters Answer Key
Answer Key
Area of Composite Shapes
Teacher Reference & Solution Guide
Grading Note: Both vertical and horizontal decompositions are valid. Primary solutions shown below with alternate splits noted.
Page 1 of 2
1 U-Channel Figure • Solutions
Total: 39 sq cm
A B C 6 cm 2 cm 2 cm 9 cm 3 cm
Rectangle A (Left Column):
2 × 6 = 12 sq cm
Rectangle B (Middle Base: 9 − 2 − 2 = 5 cm):
5 × 3 = 15 sq cm
Rectangle C (Right Column):
2 × 6 = 12 sq cm
Total Area:
12 + 15 + 12 = 39 sq cm
Alternate Horizontal Split: Bottom bar (9 × 3 = 27) + Left top (2 × 3 = 6) + Right top (2 × 3 = 6) = 27 + 6 + 6 = 39 sq cm.
2 Stepped Podium Figure • Solutions
Total: 51 sq m
A B C 4 m 8 m 5 m 3 m 3 m 3 m 9 m
Rectangle A (Left Step):
3 × 4 = 12 sq m
Rectangle B (Center Tower):
3 × 8 = 24 sq m
Rectangle C (Right Step):
3 × 5 = 15 sq m
Total Area:
12 + 24 + 15 = 51 sq m
Vertical Strategy Note: Decomposing vertically into the 3 columns is the most direct approach because each step has a clear width of 3 m.
Page 1 of 2 • Solutions continued on reverse
Answer Key
Area of Composite Shapes
Page 2 Solutions
Decomposition Check: Verify student subtracted cutout widths correctly to determine interior segments.
Page 2 of 2
3 Bridge Archway Figure • Solutions
Total: 54 sq ft
A B C 10 ft 7 ft 3 ft 3 ft 4 ft
Rectangle A (Left Leg):
3 × 7 = 21 sq ft
Rectangle B (Center Lintel: width 4 ft, height 7 − 4 = 3 ft):
4 × 3 = 12 sq ft
Rectangle C (Right Leg):
3 × 7 = 21 sq ft
Total Area:
21 + 12 + 21 = 54 sq ft
Alternate Horizontal Split: Top beam (10 × 3 = 30) + Left lower leg (3 × 4 = 12) + Right lower leg (3 × 4 = 12) = 30 + 12 + 12 = 54 sq ft.
4 Asymmetrical Notch Figure • Solutions
Total: 57 sq yd
A B C 8 yd 3 yd 3 yd 6 yd 3 yd 11 yd
Rectangle A (Left Column):
3 × 8 = 24 sq yd
Rectangle B (Center Base: 11 − 3 − 3 = 5 yd):
5 × 3 = 15 sq yd
Rectangle C (Right Column):
3 × 6 = 18 sq yd
Total Area:
24 + 15 + 18 = 57 sq yd
Alternate Horizontal Split: Bottom base (11 × 3 = 33) + Left top (3 × 5 = 15) + Right top (3 × 3 = 9) = 33 + 15 + 9 = 57 sq yd.
End of Answer Key • All 4 problem solutions verified
