# Mathematics

The sides of the pentagon are quadrupled, so they are now __ times as large. This means the area is now __ times as large. This is equivalent to an increase of __%.

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1. This is the third time this question has been answered since yesterday, each time posted by students
with a different name. Are you just switching names?

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2. I don't understand the solution, can you help me?

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3. Ok

The pentagon is made up of 5 equal isosceles triangles with a central angle of 72°, right?
Each base angle = 52°
if we let the base = 2, then the height will be:
tan52 = h/1
h = tan52
and the area of one triangle = (1/2)(2)tan52° = tan52
area of whole pentagon = 5tan52

so we are quadrupling the base, so the base is now 8
and the height is 4tan52°
area of whole pentagon = (1/2)(8)20tan52 = 80tan52

how many times larger is 80tan52 than 5tan52 ????
80tan52/(5tan52) = 16

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