📚 Practice With Worksheets
Strengthen area-reasoning skills with additional practice involving shaded regions, circles, rectangles, squares, and figures that must be decomposed into simpler shapes.
▶️ Learn With Videos
Watch the related lessons to review how subtraction, decomposition, and familiar area formulas can be used to determine shaded regions.
🛠️ How to Use This Tool
Study the diagram, identify the requested region, and determine which dimensions and area formulas are needed.
Enter the numerical area in the answer box. The correct square-unit label automatically appears beside the input.
Use the grid, formula reference, zoom controls, and progressive Reveal Structure hints when additional support is needed.
🧠 Things to Notice
Some problems require subtracting an interior area from a larger outer area, while others involve a fraction of a whole figure or a missing dimension.
A circle problem may provide the diameter instead of the radius. Remember that the radius is one-half of the diameter.
When the grid is shown, each small square represents one unit and the vertices and boundaries align with grid intersections.
📘 Vocabulary
Area: The amount of space inside a two-dimensional figure, measured in square units.
Shaded Region: The colored portion of a figure whose area must be determined.
Composite Figure: A figure made from two or more familiar geometric shapes.
Decompose: To separate a complex figure into simpler shapes whose areas can be calculated.
Difference of Areas: The result found by subtracting the area of one region from the area of another.
Radius: The distance from the center of a circle to a point on the circle.
Diameter: A segment through the center of a circle with endpoints on the circle; it is twice the radius.
Semicircle: One-half of a circle.
📐 Area Formulas and Relationships
Use the dimensions shown in the diagram to calculate the area of each familiar shape.
Rectangle: \(A=lw\)
Square: \(A=s^2\)
Triangle: \(A=\frac{1}{2}bh\)
Trapezoid: \(A=\frac{1}{2}(b_1+b_2)h\)
Circle: \(A=\pi r^2\)
Semicircle: \(A=\frac{1}{2}\pi r^2\)
When a smaller region is removed from a larger figure, subtract its area from the area of the whole figure.
\(\text{Requested Area}=\text{Whole Area}-\text{Removed Area}\)
For circle problems in this explorer, use \(\pi\approx3.14\) when instructed. Always express the final result in square units.
🔗 Share This Math Tool
Found this resource helpful? Share it with another teacher or save the link for later.
🚀 Explore More Math Tools
Browse more interactive tools for probability, statistics, algebra, geometry, ratios, and number systems.
Explore More Math Tools