SOLUTION: Estimate the area of the rectangle in square units. Each square represents 1 square unit.

Question 190624: Estimate the area of the rectangle in square units. Each square represents 1 square unit.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, I'm going to categorize the portions of the rectangle. The red portions are grid squares that are completely enclosed by the rectangle, the green portions are the corners and finally the blue regions are the edges.

Note: image is not to scale

Let's find the area of the red region:

Notice how there are 3 red squares in the middle. So the area of these three red squares is: 3*1=3 (since each square is one square unit). So this means that the area of the rectangle is at least 3 square units

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Now let's find the area of the blue region:

First, let's estimate the area of one of the blue regions that lies on top of the rectangle. One of these regions is 1 unit across and about units high (just a guess). So the area of one blue tile is square units.

Now multiply this single area by 6 (since there are 6 blue tiles that line the top and bottom) to get

So the total area of the blue tiles that line the top and bottom is about 4.5 square units

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Now let's estimate the area of the blue tiles that line the sides. The height is 1 unit and the width is about half, so the area is approximately . Double this value (there are two blue tiles on the side) to get

So the area of the lateral blue tiles is about 1 square unit

Add this to the area of the tiles that line the top/bottom to get:

So the total area of the blue tiles is about 5.5 square units.

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Finally, let's find the area of the green region:

Looking at one green tile, each tile is about units wide and units long. So this means that the area of one green tile is about square units

Multiply this area by 4 to get

So the total area of the green region is about 1.5 square units

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Now add up the three separate areas to get

Area of Red + Area of Blue + Area of Green = 3 + 5.5 + 1.5 = 10

So the total estimated area of the rectangle is about 10 square units.
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