Calculating and Estimating Area and Perimeter

Calculating and Estimating Area and Perimeter

In this lesson, we will learn:

  • How to count areas with squares and/or triangles (unit squares and half unit squares)
  • How to estimate areas of shapes on an area grid

Notes:

  • Review: finding perimeter and area for rectangular figures
Calculating and Estimating Area and Perimeter

  • How do you find the area of shapes that are not made of squares?
    • If you cut a square diagonally, you will get a triangle (half a square is a triangle)
Calculating and Estimating Area and Perimeter
    • If you cut 2 squares diagonally (2 cm2), you will get half the area (1 cm2)
    • There are other variations of getting half of a square (1/2 cm2 or 0.5 cm2)
    • There will also be cases where you won't know the exact amount shaded in one square, but you can say whether it is more or less than half

Calculating and Estimating Area and Perimeter

  • To estimate areas of a shape on a grid, we can get close to the actual area by:
    • Counting all the whole unit squares (fully shaded in or covered by the shape)
    • Counting all the half unit squares (most commonly the diagonal triangle)
    • Rounding any squares shaded more than half up to \approx 1 cm2
    • Rounding any squares shaded less than half down to \approx 0 cm2
Calculating and Estimating Area and Perimeter

Lessons

  • Introduction
    Introduction to Calculating and Estimating Area and Perimeter:
    a)
    Estimating area for triangles (using unit squares)

    b)
    Estimating area for shaded in portions of unit squares

    c)
    Example for estimating shaded area on a grid


  • 1.
    Comparing perimeter and areas of unit square rectangles
    a)
    Fill in the table for each rectangle with proper units (cm)
    Calculating and Estimating Area and Perimeter

    b)
    Using the answers from part a), answer the following questions with the letter of each rectangle:
    1. Which rectangle has the biggest perimeter? ____
    2. Which rectangle has the biggest area? ____
    3. Which rectangles have the same perimeter? ____
    4. Which rectangles have the same area? ____


  • 2.
    Estimating the area of a shaded figure using half unit squares
    Estimate the area covered by the shaded figure.
    Remember that: Calculating and Estimating Area and Perimeter and Calculating and Estimating Area and Perimeter
    a)
    Calculating and Estimating Area and Perimeter

    b)
    Calculating and Estimating Area and Perimeter


  • 3.
    Estimating the area of a shaded figure using halves of unit square doubles
    Estimate the area covered by the shaded figure.
    Remember that: Calculating and Estimating Area and Perimeter and Calculating and Estimating Area and Perimeter
    a)
    Calculating and Estimating Area and Perimeter

    b)
    Calculating and Estimating Area and Perimeter


  • 4.
    Estimating the area of a shaded figure with different proportions of unit squares
    Approximate the area of the shape by filling out the table.
    a)
    How many of each type of square is shaded in?
    Calculating and Estimating Area and Perimeter

    b)
    What is the approximate area if each square represents 1m2?
    The values of each type of square shaded in are listed:
    1. whole = 1
    2. half =1/2
    3. >> half = 1
    4. << half = 0