Geometry

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.

P is the midpoint of line BD.  AP = BP = 4 => BD = 8.

For triangle ABP  A = B = 45⁰ => 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.