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
. What is the perimeter of the base of the birdhouse?

The perimeter of the base of the birdhouse is 36 units

Step-by-step explanation:

The complete question is

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

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