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P is the midpoint of line BD.  AP = BP = 4, line AP is perpendicular to line BD, line BD is perpendicular to line DC, line AB is perpendicular to line BC .What is the area of pentagon ABCDP?

 

 Dec 17, 2021
 #1
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Triangle BAP and BDC is similar using angle angle. BP is also the midpoint og PD so PD is also 4. DC is 8 because of the similar triangles. So find the areas and add it up.

 Dec 17, 2021
 #2
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P is the midpoint of line BD.  AP = BP = 4 => BD = 8.

For triangle ABP  A = B = 45=> CBD = 450 => BCD = 450 => CD = 8

Area of pentagon ABCDPA = Area of ABP + Area of BCD = (1/2)(4*4 + 8*8) = 40 sq units.

 Dec 17, 2021

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