📚 Practice With Worksheets
Practice finding the area of rectangles, triangles, trapezoids, and composite figures with these related worksheets.
▶️ Learn With Videos
Review area formulas and build a visual understanding of how the formulas for common two-dimensional figures are connected.
🛠️ How to Use This Tool
Choose a shape, then drag it to a new location on the coordinate grid. Use the blue handles to resize the figure and observe how its dimensions change.
Select Hide answer when students should calculate the area independently before revealing the result.
Hide the controls when you need more workspace for larger figures, classroom demonstrations, or discussions about decomposing and rearranging shapes.
🧠 Things to Notice
Area measures the amount of two-dimensional space inside a figure and is expressed in square units.
The height of a triangle or parallelogram is the perpendicular distance to its base, not necessarily the length of a slanted side.
Many area formulas can be understood by decomposing, rearranging, doubling, or comparing a figure with a rectangle.
📘 Vocabulary
Area: The number of square units needed to cover a two-dimensional figure.
Square Unit: A unit used to measure area, such as one square inch or one square centimeter.
Base: The side of a figure selected as the reference side when finding area.
Height: The perpendicular distance from a base to the opposite side or vertex.
Parallel: Lines or segments in the same plane that remain the same distance apart.
Radius: The distance from the center of a circle to any point on the circle.
Decompose: To separate a figure into smaller, familiar shapes.
Composite Figure: A figure made from two or more simpler shapes.
📐 Rules / Concepts
Area formulas describe how the dimensions of a figure determine the number of square units inside it. The base and height must be measured in the same units, and the final answer should be written in square units.
Rectangles and squares use the product of the base and perpendicular height. For a square, the base and height are equal.
\(A=bh\)
\(A=s^2\)
Parallelograms can be rearranged to form rectangles. Their area uses the base and perpendicular height, not the slanted side.
\(A=bh\)
Triangles have half the area of a parallelogram or rectangle with the same base and height.
\(A=\frac{1}{2}bh\)
Trapezoids use the average length of the two parallel bases multiplied by the perpendicular height.
\(A=\frac{1}{2}(b_1+b_2)h\)
Circles use the square of the radius. A semicircle has one-half the area of a complete circle.
\(A=\pi r^2\)
\(A_{\text{semicircle}}=\frac{1}{2}\pi r^2\)
Composite figures can be divided into familiar shapes. Find each smaller area, then add or subtract the parts as needed.
\(\text{Total area}=\text{sum of the component areas}\)
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