SOLUTION: Find the perimeter and area of the figure pictured below. [Graphs generated by this script: initPicture(-6,18,-6,18);path([[0,0],[0,12.5],[3,12.5],[3,2.6],[9.8,2.6],[9.8,0],[0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the perimeter and area of the figure pictured below. [Graphs generated by this script: initPicture(-6,18,-6,18);path([[0,0],[0,12.5],[3,12.5],[3,2.6],[9.8,2.6],[9.8,0],[0      Log On


   

Question 1200389: Find the perimeter and area of the figure pictured below.

[Graphs generated by this script: initPicture(-6,18,-6,18);path([[0,0],[0,12.5],[3,12.5],[3,2.6],[9.8,2.6],[9.8,0],[0,0]]);text([0,6.25],'12.5 m','left');text([1.5,12.5],'3 m','above');text([9.8,1.3],'2.6 m','right');text([4.9,0],'9.8 m','below');]

Perimeter = __________________ m
Area = __________________  
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Answers:
Perimeter = 44.6 meters
Area = 55.18 square meters
These decimal values are exact without any rounding done to them.


Explanation:

Starting diagram

The total vertical height is 12.5 meters
The far right side small vertical piece is 2.6 meters, meaning the remaining vertical portion is 12.5-2.6 = 9.9 meters

The total horizontal width is 9.8 meters
The top side small horizontal piece is 3 meters, meaning the remaining middle horizontal portion is 9.8-3 = 6.8 meters

Let's update the diagram with those new measurements.


Perimeter = sum of the exterior sides
Perimeter = 12.5+3+9.9+6.8+2.6+9.8
Perimeter = 44.6 meters

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Another approach to find the perimeter:

Draw vertical and horizontal dashed lines like so

The vertical dashed line on the far right represents the previous vertical segment that was 9.9 meters tall.
The horizontal dashed line at the top represents the previous horizontal segment that was 6.8 meters long.

We have a rectangle after moving those sides or fences around.
Perimeter of a rectangle = 2*(length + width)
Perimeter = 2*(9.8+12.5)
Perimeter = 2*(22.3)
Perimeter = 44.6 meters

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Now to find the area

Let's revisit the original diagram and add in a red vertical line as shown below.

We'll ignore the "9.8 m" and go with the 6.8 m instead.

We have sub-divided the L shape into two rectangles
left area = 12.5*3 = 37.5
right area = 6.8*2.6 = 17.68
total area = left + right = 37.5+17.68 = 55.18 square meters

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Another way to find the area:

Revisit the diagram where we added those two dashed segments.

Let
A = area of the larger rectangle
B = area of the smaller rectangle
The idea is to find each area and then subtract those results.

A = 12.5*9.8 = 122.5
B = 9.9*6.8 = 67.32
A-B = 122.5 - 67.32 = 55.18 square meters