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Find the area of this polygon

Find the area of this polygon-example-1

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Explanation:

we need to find right-angled triangles, rectangles and squares with vertexes on grid dots. we calculate the different areas and then sum them up.

I see on the left a 1×2 right-angled triangle.

then connecting to that at the bottom a 3×1 right-angled triangle.

connecting to that on the right is another 3×1 right-angled triangle.

connecting to that on the top a 3×2 right-angled triangle.

and that left in the center a 2×1 rectangle.

remember, the area of a triangle is

baseline × height /2

the area of a rectangle is

length × width.

so, we have

1×2 / 2 = 1 unit²

3×1 / 2 = 1.5 unit²

3×1 / 2 = 1.5 unit²

3×2 / 2 = 3 units²

2×1 = 2 units²

in total that is an area of

1 + 1.5 + 1.5 + 3 + 2 = 9 units²

User Hamady
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