Question

How do you find the area of this figure?

Answer 1

The answer is 14 boxes

Explanation:

honestly the easiest way to get this is by adding all of the boxes together then adding half boxes. That's the best way to do it since there are no numbers

Answer 2

The area is 14 units².

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:

1. a square whose diagonals are length 4
2. a right triangle with legs of length 2
3. a right triangle with one leg 2 and the other leg 4.

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.

_____

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