Question

What is the surface area of this design ?

Answer 1

440 in^2 is the surface area

Answer 2

Answer: $440\ in.^2$

Step-by-step explanation:

The formula to calculate the surface area of cuboid with dimensions l by w by h is given by :-

$S.A.=2(lw+wh+hl)$

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 :-

$S.A._1=2(5\cdot5+5\cdot8+5\cdot8)=2(25+40+40)=210\ in.^2$

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 :-

$S.A._2=2(10\cdot10+10\cdot2+10\cdot2)=2(100+20+20)=280\ in.^2$

Now, the surface area of design = $S.A._1+S.A._2-2(\text{Area of base of upper block})$

$=280+210-2(5\cdot5)\\\\=490-50=440\ in.^2$

Hence, the the surface area of this design =$440\ in.^2$