How do you find the area of this figure?

The area is 14 units².

Step-by-step explanation:

You find the area by dividing the figure into parts whose area you know how to find. Then add up the areas of the parts.

In the first attachment, we have divided the figure into 3 parts:

The areas of these are

... square area: half the square of the diagonal length: (1/2)(4²) = 8

... smaller right triangle: half the product of the leg lengths: (1/2)(2)(2) = 2

... larger right triangle: same as for the smaller triangle: (1/2)(2)(4) = 4

Total area: 8 + 2 + 4 = 14 . . . . unit².

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Another way to do it is to "count squares". Here, it is fairly easy to match pieces of one square with missing peices of another square to make whole squares. Such matches are indicated in yellow in the second attachment. Whole squares are counted in red. The red and yellow squares together have an area of ...

... 9 + 5 = 14 . . . . units²