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.
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.
Answer: 84
Practice problems
1. Find the area of a rectangle with length 11 and width 6.
Show solution
- Warm-up: First identify exactly what the question is asking: Find the area of a rectangle with length 11 and width 6.
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Area = length x width.
- Check the result by substituting or estimating: the response should match 66 and make sense in the original problem.
Answer: 66
2. Find the area of a triangle with base 14 and height 5.
Show solution
- Warm-up: First identify exactly what the question is asking: Find the area of a triangle with base 14 and height 5.
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Area = 1/2 x base x height.
- Check the result by substituting or estimating: the response should match 35 and make sense in the original problem.
Answer: 35
3. Find the area of a parallelogram with base 9 and height 7.
Show solution
- Core Practice: First identify exactly what the question is asking: Find the area of a parallelogram with base 9 and height 7.
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Area = base x height.
- Check the result by substituting or estimating: the response should match 63 and make sense in the original problem.
Answer: 63
4. Find the area of a trapezoid with bases 8 and 14 and height 5.
Show solution
- Core Practice: First identify exactly what the question is asking: Find the area of a trapezoid with bases 8 and 14 and height 5.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Area = 1/2(b1 + b2)h.
- 1/2(22)(5) = 55.
- Check the result by substituting or estimating: the response should match 55 and make sense in the original problem.
Answer: 55
5. A 15 by 10 rectangle has a 5 by 4 corner removed. What area remains?
Show solution
- Challenge: First identify exactly what the question is asking: A 15 by 10 rectangle has a 5 by 4 corner removed. What area remains?
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- 150 - 20 = 130.
- Check the result by substituting or estimating: the response should match 130 and make sense in the original problem.
Answer: 130
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