An L-shaped garden is a 7 m by 8 m rectangle with an 3 m by 4 m corner rectangle removed. Sketch and find the garden area.
44 m²
Outer area 56 minus cutout 12 = 44.
Day 109Composite Polygon Areas
Standards 6.G.A.1
LEARNING TARGET
I can decompose a polygon into familiar shapes to find area.
01 · LEARN
Build the idea
Sketch the figure and label every given length. Split the region into nonoverlapping rectangles and triangles, or subtract a cutout from a larger rectangle. Add only the areas that belong to the figure.
A 8 m by 4 m rectangle has a right-triangle corner removed with perpendicular legs 2 m and 2 m. Sketch the remaining polygon and find its area.
30 m²
Whole rectangle 32; remove triangle 2; difference 30.
02 · PRACTICE
Your turn
Work in order. Start with the foundations, then build toward explanation and application.
An L-shaped garden is a 14 m by 9 m rectangle with an 8 m by 3 m corner rectangle removed. Sketch and find the garden area.
An L-shaped garden is a 8 m by 10 m rectangle with an 4 m by 6 m corner rectangle removed. Sketch and find the garden area.
An L-shaped garden is a 13 m by 8 m rectangle with an 7 m by 2 m corner rectangle removed. Sketch and find the garden area.
An L-shaped garden is a 13 m by 10 m rectangle with an 7 m by 4 m corner rectangle removed. Sketch and find the garden area.
An L-shaped garden is a 5 m by 4 m rectangle with an 3 m by 2 m corner rectangle removed. Sketch and find the garden area.
An L-shaped garden is a 7 m by 11 m rectangle with an 3 m by 7 m corner rectangle removed. Sketch and find the garden area.
A 4 m by 6 m rectangle has a right-triangle corner removed with perpendicular legs 2 m and 4 m. Sketch the remaining polygon and find its area.
A 13 m by 9 m rectangle has a right-triangle corner removed with perpendicular legs 6 m and 3 m. Sketch the remaining polygon and find its area.
A 13 m by 8 m rectangle has a right-triangle corner removed with perpendicular legs 6 m and 2 m. Sketch the remaining polygon and find its area.
A 6 m by 8 m rectangle has a right-triangle corner removed with perpendicular legs 2 m and 6 m. Sketch the remaining polygon and find its area.
03 · CHECK
Answers and reasoning
Reveal the teacher answer key
- 102 m²
Outer area 126 minus cutout 24 = 102.
- 56 m²
Outer area 80 minus cutout 24 = 56.
- 90 m²
Outer area 104 minus cutout 14 = 90.
- 102 m²
Outer area 130 minus cutout 28 = 102.
- 14 m²
Outer area 20 minus cutout 6 = 14.
- 56 m²
Outer area 77 minus cutout 21 = 56.
- 20 m²
Whole rectangle 24; remove triangle 4; difference 20.
- 108 m²
Whole rectangle 117; remove triangle 9; difference 108.
- 98 m²
Whole rectangle 104; remove triangle 6; difference 98.
- 42 m²
Whole rectangle 48; remove triangle 6; difference 42.