Active Area Decomposition Mission
Master irregular and composite area! Explore dynamic split boundaries, partition coordinates, and answer graded geometry review questions.
When dealing with irregular or composite figures, do not try to find a single complex formula. Instead, decompose (break) the shape into familiar rectangles and triangles, find their individual areas, and add them together.
Slice the composite shape vertically. This gives you a left rectangle and a right rectangle side-by-side.
Slice the composite shape horizontally. This gives you a top rectangle and a bottom horizontal base rectangle.
Adjust the **Column Height**, **Shelf Height**, and **Widths** to draw an L-shape composite figure. Click the **Decomposition Split** buttons to visually slice the shape, showing individual formulas, dimensions, and areas live!
Observe the coordinate polygon plotted on the $10 \times 10$ plane. Count the grid side units, decompose the shape into a **rectangle** and a **triangle** (by clicking the "Decompose Guide" helper), and type in its total area below!
The trapezoid vertices are located at:
A(2, 2),
B(8, 2), C(5, 7), D(2, 7).
An irregular L-shape carpet consists of a left vertical section of 8 ft × 3 ft, and a right horizontal extension of 4 ft × 2 ft. What is its **total area**?
A decorative T-shape wooden board is composed of two rectangles: a top horizontal head of 10 inches × 3 inches, and a central vertical base stem of 6 inches × 3 inches. What is the **total area**?
A custom wooden sign is shaped like a house. The bottom is a rectangle measuring 12 cm wide × 10 cm high, and the top roof is a triangle with base 12 cm and height 5 cm. What is the **total area** of the sign?
An asymmetric coordinate pentagon has vertices at $(2, 2)$, $(7, 2)$, $(7, 6)$, $(4, 8)$, and $(2, 6)$. Slicing it horizontally at $y = 6$ splits it into a bottom rectangle and a top triangle. What is the **total area**?
Geometry Practice Certified Master
Outstanding! You have mastered decomposition splits and coordinate polygon calculations.