Mathematics, 22.07.2019 04:00 huangjianhe135

What is the area of of the polygon at right?

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We can split up this polygon into three separate sections A, B, and C as seen in image below here.

So each "square" on grid has area of 1 square unit, so we just need to count blue square unit.

It's easy to count blue unit square on section C. That would be 10 square units.

Now section B is triangle so we can find area of triangle. We need base and height and lucky, it is right angle triangle so we just need to count unit length of base and height.

base is 4 unit long and height is 4 units high, so the area of B would be (1/2) ·4·4 = 8 square units

Now for section A, it's rectangle. We can just count length and width.

It has length 12 units and width 5 units, so the area of A would be 12·5 = 60 square units.

So the area of this polygon would be A + B + C = 60 + 8 + 10 = 78

Final 78 square units

Hope this helps.
What is the area of of the polygon at right?

What is the area of of the polygon at right?

Answer from: Quest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

Answer from: Quest

if you was gonna solve for a, a is a < -12

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