Area and Composite Figures
A free Geometry lesson from the “Measurement, Circles, and 3D Solids” unit, with a worked example and practice problems including step-by-step solutions.
Area measures the space inside a figure. Composite figures can be split into rectangles, triangles, parallelograms, or trapezoids, then the areas can be added or subtracted. In Measurement, Circles, and 3D Solids, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.
What you'll learn
- Find polygon area
- Break apart composite figures
- Use units carefully
Worked example
Problem. A rectangle is 12 by 8. A 3 by 4 rectangle is removed. What area remains?
- Large rectangle area: 12 x 8 = 96.
- Removed area: 3 x 4 = 12.
- Subtract: 96 - 12 = 84.
- Connect the result back to Area and Composite Figures so the geometric relationship is explicit.
Answer: 84
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Find the area of a rectangle with length 11 and width 6.
Show solution
- Area = length x width.
Answer: 66
2. Find the area of a triangle with base 14 and height 5.
Show solution
- Area = 1/2 x base x height.
Answer: 35
3. Find the area of a parallelogram with base 9 and height 7.
Show solution
- Area = base x height.
Answer: 63
4. Find the area of a trapezoid with bases 8 and 14 and height 5.
Show solution
- Area = 1/2(b1 + b2)h.
- 1/2(22)(5) = 55.
Answer: 55
5. A 15 by 10 rectangle has a 5 by 4 corner removed. What area remains?
Show solution
- 150 - 20 = 130.
Answer: 130
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