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# I need help. How do I do this problem?

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What is the area of the composite figure whose verticies has the following coordinates?

(-4,3)(2,3)(4,-1)(0,-3)(-2,-1)

Apr 25, 2019
edited by Guest  Apr 25, 2019

#1
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Ok... This is the shape (green dots)

I will give you a strategy on how to solve this, quite complicated though.

1. Use the distance formula to find the distance between all the points to find each side length of the five-sided polygon.

2. Divide the shape into three triangles.

3. Use Heron's formula to solve for the area of each triangle (using the side lengths you got from step 1)

4. Add up each triangle's area to find the total area of the shape.

This is definitely not the best way to solve this, and might be very tedious. But it still works.

Apr 25, 2019
#2
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Another way:

You can split the shape up into a parallelogram and a triangle:

https://www.desmos.com/calculator/oq7cgopnl5

Count the number of units in the lengths and heights of each shape.

And remember that

area of parallelogram  =  length of base * length of height

area of triangle  =  1/2 * length of base * length of height

Then you can calculate the area of the parallelogram and the area of the triangle.

Add the two areas together to find the total area of the figure.

(I'm pretty sure there are other ways to solve this too. )

Apr 25, 2019