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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

Why it matters: Carpeting a room, fencing a yard, and figuring paint coverage are all area and perimeter problems. The right formula depends on the shape.

Worked example

Problem. Find the area of a triangle with base 12 and height 5.

  1. Use area = 1/2 x base x height.
  2. 1/2 x 12 x 5 = 6 x 5.
  3. The area is 30 square units.
  4. Connect the calculation back to Area and Perimeter Foundations so the method, not just the arithmetic, is clear.

Answer: 30

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response). Counts include repeated prompts and variants.

Practice problems

1. Find the perimeter of a rectangle with length 8 and width 3.

Show solution
  1. Add all sides: 8 + 3 + 8 + 3.
  2. The perimeter is 22.

Answer: 22

2. Find the area of a rectangle with length 9 and width 4.

Show solution
  1. Area = length x width.
  2. 9 x 4 = 36.

Answer: 36

3. Find the area of a triangle with base 10 and height 6.

Show solution
  1. Area = 1/2 x base x height.
  2. 1/2 x 10 x 6 = 30.

Answer: 30

4. Find the area of a parallelogram with base 7 and height 5.

Show solution
  1. Area = base x height.
  2. 7 x 5 = 35.

Answer: 35

5. A square has side length 11. What is its perimeter?

Show solution
  1. A square has four equal sides.
  2. 4 x 11 = 44.

Answer: 44

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