Question

Find the surface area of the following figure.

Answer 1

`\boxed{\textsf{\pink{ Hence the TSA of the cuboid is $\sf 32x^2$}}}.`

Explanation:

A 3D figure is given to us and we need to find the Total Surface area of the 3D figure . So ,

From the cuboid we can see that there are 5 squares in one row on the front face . And there are two rows. So the number of squares on the front face will be 5*2 = 10 .

We know the area of square as ,

`\qquad\boxed{\sf Area_((square))= side^2}`

Hence the area of 10 squares will be 10x² , where x is the side length of each square. Similarly there are 10 squares at the back . Hence their area will be 10x² .

Also there are in total 12 squares sideways 6 on each sides . So their surface area will be 12x² . Hence the total surface area in terms of side of square will be ,

`\sf\implies TSA_((cuboid))= 10x^2+10x^2+12x^2\\\\\sf\implies\boxed{\sf TSA_((cuboid))= 32x^2}`

Now let's find out the TSA in terms of side . So here the lenght of the cuboid is equal to the sum of one of the sides of 5 squares .

`\sf\implies 5x = l \\\\\sf\implies x = (l)/(5) \\\\\qquad\qquad\underline\red{ \sf Similarly \ breadth }\\\\\sf\implies b = 3x \\\\\sf\implies x = ( b)/(3)`

`\rule{200}2`

Hence the TSA of cuboid in terms of lenght and breadth is :-

`\sf\implies TSA_((cuboid))= 10x^2+10x^2+12x^2\\\\\sf\implies TSA_((cuboid))= 20\bigg((l)/(5)\bigg)^2+12\bigg((b)/(3)\bigg) \\\\\sf\implies TSA_((cuboid))= 20*(l^2)/(25)+12* (b^2)/(9)\\\\\sf\implies \boxed{\red{\sf TSA_((cuboid))= (4)/(5)l^2 +(4)/(3)b^2 }}`