Length, breadth and height of a cuboid shape box of medicine is 20cm, 12 cm and 10 cm respectively. Find the surface area of vertical faces and total surface area of this box.

Given: A cuboid shape box of medicine having,

Length (l) = 20 cm

Breadth (b) = 12 cm

Height (h) = 10 cm

To find: Surface Area of vertical faces (SA) = ?

Total Surface Area of the box (cuboid) (TSA) = ?

To find Surface Area of vertical faces of cuboid:

It will be found by adding vertical sides of cuboid, i.e., front side, back side, left side and right side of the cuboid.

So, Surface Area of vertical faces = (Area of front face) + (Area of back face) + (Area of left face) + (Area of right face)

⇒ SA = lh + lh + bh + bh

⇒ SA = 2 lh + 2 bh

⇒ SA = 2(l + b)×h

⇒ SA = 2(20 + 12)×10

⇒ SA = 2 × 32 × 10

⇒ SA = 640

Thus, Surface Area of vertical faces of the box is 640 cm².

To find Total Surface Area of the box:

We have a formula for Total Surface Area of cuboid given by,

TSA = 2(lb + bh + hl)

⇒ TSA = 2(20×12 + 12×10 + 10×20)

⇒ TSA = 2(240 + 120 + 200)

⇒ TSA = 2(560)

⇒ TSA = 1120

Thus, Total Surface Area of the box is 1120 cm².

Hence, Surface Area of vertical faces of the box is 640 cm² and Total Surface Area of the box is 1120 cm².