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2 answers:
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Answer:
The perimeter of the base of the birdhouse is 36 units
Step-by-step explanation:
<u><em>The complete question is</em></u>
Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the measure of the exterior angle and the length of a diagonal that passes through the center is 12. What is the perimeter of the base of the birdhouse?
step 1
Find the measure of the interior angle
Let
x ---> the measure of the interior angle
y ---> the measure of the exterior angle
Remember that
the sum of the interior and exterior angle in any polygon is equal to 180 degrees
so
----> equation A
we have that
the measure of the interior angle is twice the measure of the exterior angle
so
----> equation B
substitute equation B in equation A
so
That means-----> The figure is a regular hexagon
step 2
Remember that
The length of the diagonal that passes through the center of the hexagon is equal to two times the length of the regular hexagon
Let
b ----> the length side of the hexagon
so
The perimeter of the hexagon is given by the formula
substitute
Answer:
Fraction of the scouts are square dancing is .
Step-by-step explanation:
Each pair is one Girl Scout and one Boy Scout.
So, to the final fraction ( of the pairs) we are going to get 1/2 from the fraction of girls and 1/2 from the fraction of boys.
Girls=
Boys=
To get the fraction of the scouts that are square dancing, we have to add the fraction of girls , with the fraction of boys.
=
=
=
=
This means that from 30 scouts , 19 are dancing.