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The vertices of a convex pentagon are \((-1, -1), (-3, 4), (1, 7), (6, 5)\) and \((3,-1)\) . What is the area of the Pentagon?

 

tertre  Mar 21, 2018

Best Answer 

 #1
avatar+7177 
+3

Here's one way.....

 

We can break the shape up into right triangles and rectangles, then get the area of each piece.

 

 

Remember   the area of a triangle  =   (1/2)(length of base)(height)

 

Add the areas together...

 

6 + 5 + 2 + 9 + 5 + 20   =   47    sq units

hectictar  Mar 21, 2018
 #1
avatar+7177 
+3
Best Answer

Here's one way.....

 

We can break the shape up into right triangles and rectangles, then get the area of each piece.

 

 

Remember   the area of a triangle  =   (1/2)(length of base)(height)

 

Add the areas together...

 

6 + 5 + 2 + 9 + 5 + 20   =   47    sq units

hectictar  Mar 21, 2018
 #2
avatar+92928 
+2

I like Hectictar's method better   but here is a different way.

 

Divide the pentagon inot 3 triangles. Find the lengths of all the sides of all the triangles.

Then find the areas, one at a time, using Heron's formula.

 

https://www.youtube.com/watch?v=svWYgZs33bA

Melody  Mar 21, 2018

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