How to find the length of the diagonal of a pentagon - Intermediate Geometry
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What is the length of a diagonal of a pentagon with side length of 20 centimeters (to the nearest tenth)?
What is the length of a diagonal of a pentagon with side length of 20 centimeters (to the nearest tenth)?
Let 
be the length fo a diagonal.
One interior angle of a pentagon measures
A diagonal of this pentagon, along with two sides, forms an isosceles triangle with sides 20, 20 and 
; the side of length 
is opposite the angle of measure 
, and each side of length 20 is opposite an angle of measure 
.
The Law of Sines helps us to determine 
:
Let
One interior angle of a pentagon measures
A diagonal of this pentagon, along with two sides, forms an isosceles triangle with sides 20, 20 and
The Law of Sines helps us to determine
Compare your answer with the correct one above
In the pentagon below, the length of 
is one-third that of 
. Find the length of diagonal 
.
In the pentagon below, the length of
Start by using the Pythagorean theorem to find the length of 
.
Since 
is one-third the length of 
, we know that the length of 
must be 
.
Now, notice that the pentagon is made up of one rectangle and two right triangles.
Focus on rectangle 
. We can find the length of 
by adding together the lengths of 
and 
.
Since we are working with a rectangle, we know that 
. Thus, we can use the Pythagorean Theorem again to find the length of 
.
Make sure to round to two places after the decimal.
Start by using the Pythagorean theorem to find the length of
Since
Now, notice that the pentagon is made up of one rectangle and two right triangles.
Focus on rectangle
Since we are working with a rectangle, we know that
Make sure to round to two places after the decimal.
Compare your answer with the correct one above