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if the length of the cuboid is 1/2 of the perimeter of square and breadth of the cuboid is 1/4 of the perimeter of the square and height of the cuboid is 3/2 of the side of the square if the side of the square is equal to 1/2 of the length of the rectangle if the breadth of the rectangle is 1/4 of the area of the rectangle which is 64cm2 then find the lateral surface area of the cuboid.

if the length of the cuboid is 1/2 of the perimeter of square and breadth of the cuboid is 1/4 of the perimeter of the square and height of the cuboid is 3/2 of the side of the square if the side of the square is equal to 1/2 of the length of the rectangle if the breadth of the rectangle is 1/4 of the area of the rectangle which is 64cm2 then find the lateral surface area of the cuboid. Correct Answer 36cm<sup>2</sup>

Solution:

Concept:

Area of rectangle = length × breadth 

Lateral surface area of cuboid = 2 × (length + breadth) × height 

Perimeter of square = 4 × side of the square

Given: 

Length of rectangle = (area of rectangle)/breadth of rectangle

breadth = 1/4 × (area of rectangle)

Breadth = 1/4 × 64 = 16cm

Length of rectangle = 4cm

side of square  = 1/2 × (Length of rectangle)

side of square = 1/2 × 4 = 2cm

perimeter of square = 4 × side of square 

perimeter of square = 4 × 2 = 8cm

Length of cuboid = 1/2 × (perimeter of square)

Length of cuboid = 1/2 × 8 = 4cm

breadth of cuboid = 1/4 × (perimeter of square)

breadth of cuboid = 1/4 × 8 = 2cm

height of cuboid = 3/2 × side of square 

height of cuboid = 3/2 × 2 = 3cm

Lateral surface area of cuboid = 2 × (length + breadth) × height 

Lateral surface area of cuboid = 2 × (4 + 2) × 3

Lateral surface area of cuboid = 2 × 6 × ​3 = 36cm2

∴ Lateral surface area of cuboid = 36cm2

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