Question

Area of polygon with coordinates of (4,6), (6,-1), (3,-5), (-6,-4), (-6,3), (-3,6)

Answer 1

110 square units

Explanation:

There are several ways you can go at this. One of them is to use a formula that calculates area based on the coordinate values. That would be ...

`A=(1)/(2)|\sum\limits_(k=1)^n{x_k(y_(k-1)-y_(k+1))}|`

where the index values of y wrap around. For the coordinates in the order given, the area is ...

A = (1/2)(4(6+1) +6(6+5) +3(-1+4) -6(-5-3) -6(-4-6) -3(3-6))

= (1/2)(28 +66 +9 +48 +60 +9)

= (1/2)(220) = 110 . . . . square units

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Another way to approach the problem is to find the area of the bounding rectangle, 12×11 = 132, and subtract the areas of the corner triangles. Each of those has an area that is half the product of base and height. The area found this way (clockwise from upper left) is ...

A = 132 - (1/2)(3·3) -(1/2)(2·7) -(1/2)(3·4) -(1/2)(9·1)

= 132 -4.5 -7 -6 -4.5 = 110 . . . . square units