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This lesson deals with perimeter as it applies to triangles and quadrilaterals.

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Perimeter is the distance (or length) around the outside of a closed figure. It can be thought of as a "path" that surrounds a two-dimensional shape.

Shown below are some familiar perimeters expresses as "formulas".

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In general, the "formula" for finding perimeter
is to simply add the lengths of all of the line segments.

While perimeter sounds like a simple concept, it can be challenging when a question requires the use of past skills such as the Pythagorean Theorem, trigonometry, special right triangle formulas, the distance formula, or other concepts, to find lengths of individual segments.
Let's take a look at some examples.

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1. Find the perimeter of ΔABC.

Solution: We need to find the missing side from A to B.
ΔABD is a 30º-60º-90ºΔ, where the side opposite the 30º angle will be half of the hypotenuse. Since 7 is half of 14, we know that the hypotenuse from A to B equals 14".

Perimeter of ΔABC: 18 + 20 + 14 = 52"



2. Find the perimeter of trapezoid TRAP.

Solution: We need to find the missing side from A to P.
Drop a perpendicular from A to the bottom side, forming a right triangle. This new height will be parallel to the side from T to R and will be of the same length (4").
The side from T to P will now be divided into sections of 6" and 3".
A 3-4-5 right triangle (a Pythagorean Theorem triple) has been formed.
AP = 5.

Perimeter of TRAP: 6 + 5 + 9 + 4 = 24"

 

3. Find the perimeter of ΔABC to the nearest tenth.

Solution: We need to find BC and DC. We need to use trigonometry. (The "nearest tenth" was a hint.) Perimeter of ΔABC:
17 + 28.3 + 24 + 8 = 77.3

 

 

4. Find the perimeter of ΔABC to the exact measurement. Do not round.

Solution: We know BC = 12 by counting.
We need to find AB and AC.

Using the Distance Formula:

Perimeter of ΔABC:

 


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