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Lesson Plan 5: Area

Introduction
In this lesson students practice calculating areas of different geometric figures within the context of a problem-based learning scenario. They will use these skills in the M.A.R.S. mission to make important decisions concerning the location of the base.

Duration

30 minutes

Formulas

Area of a rectangle: A = B H
B = base
H = height

Area of a triangle: A = B H
                                        2

Area of a circle: A = π r2

Area of a quadrilateral: A = B (H1 + H2)
                                                     2

pi: (π) 3.14

Radius (r): a line extending from the center of a circle or sphere to the circumference (outside boundary)

Materials

  • Calculating Areas worksheet

  • Pencil

  • Calculator (optional)

Procedure

  1. Review with the students the formulas for the areas of different geometric figures.
  2. Check for understanding of vocabulary involved in the formulas.
  3. Read the problem activity that follows with the class before they begin work.

Problem Activity
You and your school nature club are trying to raise money for a club field trip to the Amazon rain forest. You have agreed to landscape the school grounds and plant flower bulbs to bloom in the spring.

The school board wants the bulbs planted in a very specific way so the new bulbs blend in with the existing landscaping.

They want the largest area planted with tulips, the next largest area with daffodils, the third largest area with crocuses, and the three smallest areas are to be planted with wildflower bulbs.

There are six areas to be planted, but you and your club have a problem! All of the areas are of different sizes and shapes! You will need to calculate the areas before you plant the bulbs so you plant the correct type of bulb in the correct area!

You measure each area to be planted and now have the following dimensions:  

circle rectangle  triangle  quadrilateral
r = 3.5 meters B = 5 meters
H = 3 meters
B = 6 meters
H = 2 meters
B = 2 meters
H1 = 2 meters
H2 = 3 meters
circle triangle    
r =  5 meters B = 4 meters
H = 6 meters
   

Directions

  1. Calculate the area of each shape to be landscaped. Use the space below the table to show your work.
  2. Complete the following table listing the area and the type of flower bulb you will plant in each location. Work carefully! Your club will not get paid if you are wrong!
Location Area (m2) Type of Flower Bulb Planted
Circle #1    
Circle #2    
Rectangle    
Triangle #1    
Triangle #2    
Quadrilateral    

  

Answers:

Circle #1 = (3.14) (12.25) 
               = 38.465 m2
Triangle #1 = 12/2 
                   = 6 m2
   
Circle #2 = (3.14) (25) 
               = 78.5 m2 
Triangle #2 = 24/2
                   = 12 m2
   
Rectangle = (5) (3)  
                 = 15 m2 
Quadrilateral = 10/2
                      = 5 m2

                                                                              

Location Area (m2) Type of Flower Bulb Planted
Circle #1 38.465 daffodils
Circle #2 78.5 tulips
Rectangle 15 crocuses
Triangle #1 6 wildflowers
Triangle #2 12 wildflowers
Quadrilateral 5 wildflowers
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