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A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the lateral surface area of the pyramid?
1. x2
2. 0.75x2
3. 0.50x2
4. 0.25x2

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Correct Answer - Option 4 : 0.25x2

Concept:

For square pyramid

Lateral surface area of the pyramid = 4 × area of one of the triangles of the pyramid.

perimeter of a square  = 4 × Side of a square

Calculation:

Given,

Square pyramid has a base perimeter = X

perimeter of a square  = 4 × Side of a square

∴ Side of the square base = X/4

The slant height  = half of the perimeter.= X/2

we know that

Perpendicular height of the triangles = Slant height of the pyramid = X/2

Base of the triangle = Side of the square base = X/4

Lateral surface area of the pyramid = 4 × area of one of the triangles of the pyramid.

Lateral surface area of the pyramid = 4 × ½ × base × height

Lateral surface area of the pyramid = 2 × (x/4) × (x/2) = 0.25x2

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