Area and perimeter of parallelograms

Area and perimeter of parallelograms

Lessons

In this lesson, we will learn:

  • The basic properties of the shape of the parallelogram
  • How to understand and calculate the perimeter of a parallelogram
  • How to understand and calculate the area of a parallelogram

Notes:

  • A parallelogram is a 2D shape with 4 straight sides
    • Each pair of sides (across from each other) are parallel and the same length
    • The internal angles are not right angles (90°); otherwise it would be a rectangle
      • Opposite angles are the same size

2D Shapes: Area and Perimeter of Parallelograms

    • A special parallelogram with all sides of equal length is called a rhombus

2D Shapes: Area and Perimeter of Parallelograms

  • The perimeter is the exact distance around the shape.
    • Perimeter is a 1D (one-dimensional) quantity
      • It uses units such as meters (m, cm, mm, km), miles (mi), yards (yd), or inches and feet (in and ft)

    • For parallelograms, the formula is written as:
      • Pparallelogram = (2×a)+(2×b) ( 2 \, \times \,a) \, + \, (2\, \times \, b)
        • Where aa is the length of one of the sides, and bb is the length of the other side

  • The area is the space that is covered by the shape.
    • Area is a 2D (two-dimensional) quantity
      • It uses squared units such as square meters (m2, cm2, mm2, km2), square miles (mi2), square yards (yd2), or square inches and feet (in2 and ft2)

    • For parallelograms, the formula is written as:
      • Aparallelogram = b×h b \, \times \, h
        • Where bb is base, and hh is height

    • A parallelogram’s height is not the same as the slant (side) length.

2D Shapes: Area and Perimeter of Parallelograms
  • Introduction
    Introduction to Area and Perimeter of Parallelograms:
    a)
    What are the basic properties of a parallelogram?

    b)
    How do you calculate the perimeter of a parallelogram?

    c)
    How do you calculate the area of a parallelogram?


  • 1.
    Perimeter of Parallelograms
    Calculate the perimeter of each parallelogram.
    a)

    2D Shapes: Area and Perimeter of Parallelograms

    b)

    2D Shapes: Area and Perimeter of Parallelograms

    c)

    2D Shapes: Area and Perimeter of Parallelograms


  • 2.
    Area of Parallelograms
    Calculate the area of each parallelogram.
    a)

    2D Shapes: Area and Perimeter of Parallelograms

    b)

    2D Shapes: Area and Perimeter of Parallelograms

    c)

    2D Shapes: Area and Perimeter of Parallelograms


  • 3.
    Perimeter and Area of Compound Parallelograms
    Calculate the perimeter and area of each compound shape. Break down the complex shapes into components (parallelograms and other polygons) first!
    a)

    2D Shapes: Area and Perimeter of Parallelograms

    b)

    2D Shapes: Area and Perimeter of Parallelograms

    c)

    2D Shapes: Area and Perimeter of Parallelograms


  • 4.
    Parallelograms Word Problem - 1
    Sophia wants to make a special picture frame using parallelograms. It will use four of the same parallelograms with the measurements: 8cm along the base and 3cm in height.

    2D Shapes: Area and Perimeter of Parallelograms
    a)
    What is the area of the picture frame?

    b)
    If the slanted part of the parallelogram is 5cm, what is the perimeter of the picture frame? Do not count the edges of the parallelograms that are glued together.