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# pentagon

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In pentagon ABCDP, AB = BC = CD = 4, angle ABC = anlge BCD = 90, AP = DP, angle APD = 90.  In simple radical form, what is the perimeter of pentagon ABCDP ?

Dec 13, 2020

#1
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In pentagon ABCDP, AB = BC = CD = 4, angle ABC = anlge BCD = 90, AP = DP, angle APD = 90.  In simple radical form, what is the perimeter of pentagon ABCDP ?

Hello Guest!

$$p=3\cdot 4+2\cdot \frac{4}{\sqrt{2}}=12+2\cdot \frac{4}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}$$

$$p=12+4\cdot\sqrt{2}$$

$$p=4(3+\sqrt{2})=17.657$$

!

Dec 14, 2020
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Perimeter    P = √144 + √32 = 17.65685425

Dec 14, 2020