Hello!
a. rectangular prism:
larger side area: 9*4 = 36 *2 sides = 72cm²
smaller side area: 8*4 = 32*2 sides = 64 cm²
base and top area: 9*8 = 72*2 = 144cm²
rectangular prism: 72 + 64 + 144 = 280 cm²
b. triangular prism:
smaller rectangular side (base): 3*5 = 15cm²
triangular sides: 4*3 = 12cm² (6cm² each side)
rectangle in black: 5*4 = 20cm²
triangular prism: 15 + 12 + 20 = 47cm²
c. overlap (rectangle in black):
as we calculated above, 5*4 = 20cm²
d. composite object:
attention, we can't just sum rectangular + triangular because it has a common side, and it would be counted twice. So, let's calculate each figure again, considering that side just one time:
triangular prism (equal above): 47cm²
smaller rectangular side (base): 3*5 = 15cm²
triangular sides: 4*3 = 12cm² (6cm² each side)
rectangle in black: 5*4 = 20cm²
rectangular prism: 124cm²
larger side area: 9*4 = 36 *1 side = 36cm²
+ 4*4 = 16cm² of the other side (disregarding the overlap)
smaller side area: 8*4 = 32*2 sides = 64 cm²
base and top area: 9*8 = 72*2 = 144cm²
composite object 47 + 124 = 171cm²