Answer: ![440\ in.^2](https://tex.z-dn.net/?f=440%5C%20in.%5E2)
Step-by-step explanation:
The formula to calculate the surface area of cuboid with dimensions l by w by h is given by :-
![S.A.=2(lw+wh+hl)](https://tex.z-dn.net/?f=S.A.%3D2%28lw%2Bwh%2Bhl%29)
From the given picture, the dimensions of upper block (cuboid) is 5 in. by 5 in. by 8 in.
Then the surface area of the upper block is given by :-
![S.A._1=2(5\cdot5+5\cdot8+5\cdot8)=2(25+40+40)=210\ in.^2](https://tex.z-dn.net/?f=S.A._1%3D2%285%5Ccdot5%2B5%5Ccdot8%2B5%5Ccdot8%29%3D2%2825%2B40%2B40%29%3D210%5C%20in.%5E2)
Also, the dimensions of lower block (cuboid) is 10 in. by 10 in. by 2 in.
Then the surface area of the upper block is given by :-
![S.A._2=2(10\cdot10+10\cdot2+10\cdot2)=2(100+20+20)=280\ in.^2](https://tex.z-dn.net/?f=S.A._2%3D2%2810%5Ccdot10%2B10%5Ccdot2%2B10%5Ccdot2%29%3D2%28100%2B20%2B20%29%3D280%5C%20in.%5E2)
Now, the surface area of design = ![S.A._1+S.A._2-2(\text{Area of base of upper block})](https://tex.z-dn.net/?f=S.A._1%2BS.A._2-2%28%5Ctext%7BArea%20of%20base%20of%20upper%20block%7D%29)
![=280+210-2(5\cdot5)\\\\=490-50=440\ in.^2](https://tex.z-dn.net/?f=%3D280%2B210-2%285%5Ccdot5%29%5C%5C%5C%5C%3D490-50%3D440%5C%20in.%5E2)
Hence, the the surface area of this design =![440\ in.^2](https://tex.z-dn.net/?f=440%5C%20in.%5E2)