Verified Answer :

  1. find the area of the rectangle
    2. find the area of the triangle 
    3. add the areas for the total area

    1. area of a rectangle = lw = 8x4 = 32cm
    2. area of triangle = 1/2bh
        the height is the line drawn from the vertex A to the center of side BE
        the base is 1/2 the length of side BE therefore  base = 4
        because the hypotenuse is 5 and the height is 4 the laws of the pythagorean   theorem state that the base equals 3 (3-4-5 right triangle) 
       Therefore the area = 1/2(3)(4)= 1/2(12) =6cm
    3. The total area equals 32cm + 6cm =38cm