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# help! please! .....

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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? Mar 21, 2018

### Best Answer

#1
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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

Mar 21, 2018

### 2+0 Answers

#1
+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
+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

Mar 21, 2018