Apply Area Concepts to Solve Problems

Decompose compound figures into simpler shapes and calculate total area for real-world problems like floor plans and gardens.

6.GR.A.1 · Area, Surface Area & Volume
Level
Guided practice with vocabulary support

🟠 Level 0 — Extra Support

Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
W

Warm-Up

2 questions
Warm-Up 1
What is a compound figure?
Vocabulary: A compound figure (also called a composite figure) is a shape made up of two or more simpler shapes put together, like rectangles and triangles.
✓Correct! A compound figure is made of two or more simpler shapes combined together.
✗A compound (composite) figure is a shape made of two or more simpler shapes. The answer is B.
Warm-Up 2
To find the total area of a compound figure, you should:
Strategy: Decompose means to break apart. Split the compound figure into shapes you know (rectangles, triangles, parallelograms), find each area, then add them up.
✓Correct! Decompose the compound figure, find each smaller area, then add them together.
✗To find the area of a compound figure: break it into simpler shapes, find each area, and add. The answer is C.
P

Practice

5 questions
Practice 1
Find the total area of this L-shaped figure.
Strategy: Decompose the L-shape into two rectangles. Find the area of each, then add.
Rectangle 1: 10 ft × 4 ft. Rectangle 2: 6 ft × 3 ft.
10 ft 4 ft 6 ft 3 ft Rect 1 Rect 2
Rect 1 area: ft²
Rect 2 area: ft²
Total area: ft²

Sentence frame: "Rect 1 = ___ × ___ = ___. Rect 2 = ___ × ___ = ___. Total = ___ + ___ = ___."

✓Correct! 10 × 4 = 40 and 6 × 3 = 18. Total = 40 + 18 = 58 ft².
✗Rect 1 = 10 × 4 = 40. Rect 2 = 6 × 3 = 18. Total = 40 + 18 = 58 ft².
Practice 2
A figure is made of a rectangle (12 m × 5 m) with a triangle on top (base 12 m, height 4 m). What is the total area?
Steps: 1) Rectangle area = 12 × 5. 2) Triangle area = ½ × 12 × 4. 3) Add them together.
12 m 5 m 4 m rectangle triangle
Show both areas:

Sentence frame: "Rectangle = ___ × ___ = ___. Triangle = ½ × ___ × ___ = ___. Total = ___ + ___ = ___."

✓Correct! Rectangle = 60 m². Triangle = 24 m². Total = 60 + 24 = 84 m².
✗Rectangle = 12 × 5 = 60. Triangle = ½ × 12 × 4 = 24. Total = 60 + 24 = 84 m². The answer is A.
Practice 3
Which decomposition correctly breaks this compound shape into simpler parts?
Remember: When you decompose a figure, you split it along straight lines into shapes like rectangles, triangles, or trapezoids — shapes whose area formulas you know.
top bar stem
✓Correct! This T-shape is best decomposed into two rectangles: a wide top bar and a narrow stem.
✗The T-shape splits naturally into one wide rectangle on top + one narrow rectangle below. The answer is A.
Practice 4
A classroom floor plan is a rectangle 30 ft × 20 ft with a rectangular closet (5 ft × 4 ft) built into one corner. What is the usable floor area?
Strategy: Find the total rectangle area, then subtract the closet area. Usable area = Total − Closet.
closet 5×4 30 ft 20 ft
Usable area = ft²
Show your work:

Sentence frame: "Total area = ___ × ___ = ___. Closet = ___ × ___ = ___. Usable = ___ − ___ = ___."

✓Correct! 30 × 20 = 600. Closet = 5 × 4 = 20. Usable = 600 − 20 = 580 ft².
✗Total = 600. Closet = 20. Usable = 600 − 20 = 580 ft².
Practice 5
A garden is shaped like a rectangle (8 m × 6 m) with a triangular section added on one end (base 6 m, height 3 m). What is the total garden area?
Steps: 1) Rectangle area = 8 × 6 = 48. 2) Triangle area = ½ × 6 × 3 = 9. 3) Total = 48 + 9.
8 m 6 m 3 m
Total area = m²
Show your work:

Sentence frame: "Rectangle = ___ × ___ = ___. Triangle = ½ × ___ × ___ = ___. Total = ___ + ___ = ___."

✓Correct! Rectangle = 48 m². Triangle = 9 m². Total = 48 + 9 = 57 m².
✗Rectangle = 8 × 6 = 48. Triangle = ½ × 6 × 3 = 9. Total = 48 + 9 = 57 m².
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Challenge

1 question
Challenge
Mr. Neft wants to tile his patio. The patio is a large rectangle (20 ft × 12 ft) with a square fountain (4 ft × 4 ft) in the center that will not be tiled. If each tile covers 2 ft², how many tiles does he need?
Multi-step: 1) Find the patio area. 2) Subtract the fountain area. 3) Divide by tile size (2 ft²) to get the number of tiles.
fountain 4×4 20 ft 12 ft
Tiling area: ft²
Number of tiles:
Show all steps:

Sentence frame: "Patio area = ___ × ___ = ___. Fountain = ___ × ___ = ___. Tiling area = ___ − ___ = ___. Tiles = ___ ÷ ___ = ___."

✓Excellent! Patio = 240. Fountain = 16. Tiling area = 224 ft². Tiles = 224 ÷ 2 = 112 tiles.
✗Patio = 20 × 12 = 240. Fountain = 4 × 4 = 16. Tiling area = 240 − 16 = 224 ft². Tiles = 224 ÷ 2 = 112.