📚 Practice With Worksheets
Strengthen composite-area skills with additional practice, mixed figures, and a convenient area-formulas reference sheet.
▶️ Learn With Videos
Watch the related lessons to review how semicircles, trapezoids, parallelograms, and other familiar shapes combine to form composite figures.
🛠️ How to Use This Tool
Choose a problem family, examine the dimensions, and decompose the composite figure into familiar shapes.
Calculate the area of each component, enter the total area in square units, and select Check Answer. After the first valid attempt, Show Solution becomes available.
Use New Problem to generate another figure. The session panel tracks correct responses, attempted problems, and overall accuracy.
🧠 Things to Notice
A composite figure can be separated into simpler shapes that share boundaries but do not overlap.
The dashed segment represents a perpendicular height. A height is measured at a right angle to its corresponding base.
For a semicircle, the labeled straight side is the diameter, so divide it by 2 before using the radius in the area formula.
📘 Vocabulary
Area: The number of square units needed to cover a two-dimensional region.
Composite Figure: A figure made by joining two or more familiar geometric shapes.
Component Shape: One of the simpler shapes used to form a composite figure.
Decompose: To separate a complex figure into simpler, non-overlapping shapes.
Base: A selected side of a figure used with its corresponding height in an area formula.
Height: The perpendicular distance from a base to the opposite side or vertex.
Perpendicular: Intersecting at a right angle of \(90^\circ\).
Rectangle: A quadrilateral with four right angles.
Triangle: A polygon with three sides and three angles.
Parallelogram: A quadrilateral with two pairs of parallel opposite sides.
Trapezoid: A quadrilateral with at least one pair of parallel sides.
Semicircle: Half of a circle formed by a diameter and one-half of the circle's circumference.
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.
Square Units: Units used to measure area, such as square centimeters or square inches.
📐 Area Formulas and Composite Figures
Use the formula that matches each component shape. In the formulas below, \(b\) represents a base, \(h\) represents a perpendicular height, \(l\) represents length, \(w\) represents width, and \(r\) represents radius.
Rectangle
\(A=lw\)
Triangle
\(A=\frac{1}{2}bh\)
Parallelogram
\(A=bh\)
Trapezoid
\(A=\frac{1}{2}(b_1+b_2)h\)
Semicircle
\(A=\frac{1}{2}\pi r^2\)
Radius From Diameter
\(r=\frac{d}{2}\)
When the component regions do not overlap, add their areas to find the total area of the composite figure.
\(A_{\text{composite}}=A_1+A_2+\cdots+A_n\)
Always attach square units to the final answer. When using \(\pi\), follow the directions for whether to leave the answer in terms of \(\pi\) or use a decimal approximation.
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