Area and Perimeter Foundations
A free Pre-Algebra lesson from the “Geometry Foundations” unit, with a worked example and practice problems including step-by-step solutions.
Perimeter measures distance around a figure. Area measures the amount of surface inside a figure. Rectangles use length times width, parallelograms use base times height, and triangles use one-half times base times height. In Geometry Foundations, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Find perimeter of polygons
- Find area of rectangles, triangles, and parallelograms
- Break composite figures into familiar parts
Worked example
Problem. Find the area of a triangle with base 12 and height 5.
- Use area = 1/2 x base x height.
- 1/2 x 12 x 5 = 6 x 5.
- The area is 30 square units.
- Connect the calculation back to Area and Perimeter Foundations so the method, not just the arithmetic, is clear.
Answer: 30
Practice problems
1. Find the perimeter of a rectangle with length 8 and width 3.
Show solution
- Warm-up: First identify exactly what the question is asking: Find the perimeter of a rectangle with length 8 and width 3.
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Add all sides: 8 + 3 + 8 + 3.
- The perimeter is 22.
- Check the result by substituting or estimating: the response should match 22 and make sense in the original problem.
Answer: 22
2. Find the area of a rectangle with length 9 and width 4.
Show solution
- Warm-up: First identify exactly what the question is asking: Find the area of a rectangle with length 9 and width 4.
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Area = length x width.
- 9 x 4 = 36.
- Check the result by substituting or estimating: the response should match 36 and make sense in the original problem.
Answer: 36
3. Find the area of a triangle with base 10 and height 6.
Show solution
- Warm-up: First identify exactly what the question is asking: Find the area of a triangle with base 10 and height 6.
- 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.
- 1/2 x 10 x 6 = 30.
- Check the result by substituting or estimating: the response should match 30 and make sense in the original problem.
Answer: 30
4. Find the area of a parallelogram with base 7 and height 5.
Show solution
- Core Practice: First identify exactly what the question is asking: Find the area of a parallelogram with base 7 and height 5.
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Area = base x height.
- 7 x 5 = 35.
- Check the result by substituting or estimating: the response should match 35 and make sense in the original problem.
Answer: 35
5. A square has side length 11. What is its perimeter?
Show solution
- Core Practice: First identify exactly what the question is asking: A square has side length 11. What is its perimeter?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- A square has four equal sides.
- 4 x 11 = 44.
- Check the result by substituting or estimating: the response should match 44 and make sense in the original problem.
Answer: 44
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