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Area games

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Problem Solving - devise a strategy
Spatial Reasoning - game is played on a 12x12 grid

Common Core Connection for Grades 3 and 4

Recognize area as an attribute of plane figures and understand area measurement.
Relate area to the operations of multiplication and addition.
Solve real world and mathematical problems involving perimeters of polygons.
Apply area and perimeter formulas for rectangles to real world problems.

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Problem Solving - devise a strategy Spatial Reasoning - game is played on a 12x12 grid Common Core Connection for Grades 3 and 4 Recognize area as an attribute of plane figures and understand area measurement. Relate area to the operations of multiplication and addition. Solve real world and mathematical problems involving perimeters of polygons.

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Compare Area and Perimeter

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Compare the areas and perimeters of rectangles when given a context or picture.

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Intro to area and unit squares (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Math is Fun-Area

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Example:

These shapes all have the same area of 9:

It helps to imagine how much paint would cover the shape.

Area of Simple Shapes

There are special formulas for certain shapes:

Example: What is the area of this rectangle?

The formula is:

The width is 5, and the height is 3, so we know w = 5 and h = 3:

Area = 5 × 3 = 15

Learn more at Area of Plane Shapes.

Area by Counting Squares

We can also put the shape on a grid and count the number of squares:

The rectangle has an area of
15

Example: When each square is 1 cm on a side, then the area is (15 square cm)

Approximate Area by Counting Squares

Sometimes the squares don't match the shape exactly, but we can get an "approximate" answer.

One way is:

Like this:

This pentagon has an area of approximately 17

Or we can count one square when the areas seem to add up.

Example: Here the area marked " 4" seems equal to about 1 whole square (also for " 8"):

This circle has an area of approximately 14

But using a formula (when possible) is best:

Example: The circle has a radius of 2.1 meters:

The formula is:

Where:

The radius is 2.1m, so:

So the circle has an area of 13.85 square meters (to 2 decimal places)

Area of Difficult Shapes

We can sometimes break a shape up into two or more simpler shapes:

Example: What is the area of this Shape?

Let's break the area into two parts:

Part A is a square:

Part B is a triangle. Viewed sideways it has a base of 20m and a height of 14m.

So the total area is:

Area by Adding Up Triangles

We can also break up a shape into triangles:

Then measure the base ( b) and height ( h) of each triangle:

Then calculate each area (using Area = ½b × h) and add them all up.

Area by Coordinates

When we know the coordinates of each corner point we can use the Area of Irregular Polygons method.

There is an Area of a Polygon by Drawing Tool that can help too.

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These shapes all have the same area of 9: It helps to imagine how much paint would cover the shape. There are special formulas for certain shapes: The formula is: The width is 5, and the height is 3, so we know w = 5 and h = 3: Area = 5 × 3 = 15 Learn more at Area of Plane Shapes.