There are four primary strategies for determining the area of two-dimensional figures and shapes: a) counting square units, b) subdividing the shape into pieces, finding the areas of the pieces and adding the areas together, c) enclosing the shape in a rectangle, finding the area outside of the shape but inside the rectangle and subtracting, and d) using a formula. Explain each strategy. Use an example for each.

Given below

Step-by-step explanation:

a) if we look at the picture then we can find by counting the square units. In each box there are 3.5 square units along the breadth. There are 3 square units along the length . Counting these gives (3*3.5= 10.5 ) 10.5 square units for each box. Adding the 10.5 +10.5+10.5+10.5 = 42 square units gives the area of the inner rectangle.

b) There are 4 boxes and the total area of the these boxes will be 4*10.5= 42 square units.

Area of 1 box = 3*3.5= 10.5

c)  The area of the outer rectangle = 8*12= 96 square units.

The area between the two rectangles along the breadth = 3*7= 21 of one side.

The area between the two  sides along the length = 6*1= 6 square units.

Subtracting 21+21+6+6= 54  from 96 gives  42 square units

d)  Area= length *breadth

           = 6* 7= 42 square units.

Hence by all four methods the total area remains the same.

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equal to

step-by-step explanation: