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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.

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.

Answer: 30

Practice problems

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

Show solution
  1. Warm-up: First identify exactly what the question is asking: Find the perimeter of a rectangle with length 8 and width 3.
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Add all sides: 8 + 3 + 8 + 3.
  4. The perimeter is 22.
  5. 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
  1. Warm-up: First identify exactly what the question is asking: Find the area of a rectangle with length 9 and width 4.
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Area = length x width.
  4. 9 x 4 = 36.
  5. 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
  1. Warm-up: First identify exactly what the question is asking: Find the area of a triangle with base 10 and height 6.
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Area = 1/2 x base x height.
  4. 1/2 x 10 x 6 = 30.
  5. 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
  1. Core Practice: First identify exactly what the question is asking: Find the area of a parallelogram with base 7 and height 5.
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Area = base x height.
  4. 7 x 5 = 35.
  5. 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
  1. Core Practice: First identify exactly what the question is asking: A square has side length 11. What is its perimeter?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. A square has four equal sides.
  4. 4 x 11 = 44.
  5. 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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