Answer: surface area = 440 in²
Step-by-step explanation:
The given solid is made up of two cuboids. The formula for determining the surface area of a cuboid is expressed as
Surface area = 2lw + 2lh + 2wh
Where
l, w and h are the length, width and height of the cuboid.
Considering the cuboid at the top, its base will not be added. Therefore, the surface area would be
lw + 2lh + 2wh
= 5 × 5 + 2(8 × 5) + 2(8 × 5)
= 25 + 80 + 80
= 185 in²
Considering the box at the base, we would determine the surface area and subtract the area of the base of the first box.
Surface area of bottom box is
2(10 × 10) + 2(10 × 2) + 2(10 × 2)
= 200 + 40 + 40 = 280 in²
The area of the base of the first box is 5 × 5 = 25 in²
Surface area of the bottom box is 280 - 25 = 255 in²
Total surface area of the design is
Area of first box + area of second box
= 185 + 255 = 440 in²
