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If base of right pyramid is a square and area of a slant surface of the pyramid is 24 cm2 and slant triangle perpendicular height of the pyramid is 6 cm, then what will be the ratio of total slant surface area to the base area of the pyramid?

If base of right pyramid is a square and area of a slant surface of the pyramid is 24 cm2 and slant triangle perpendicular height of the pyramid is 6 cm, then what will be the ratio of total slant surface area to the base area of the pyramid? Correct Answer 3 : 2

GIVEN:

Area of a slant surface of the pyramid = 24 cm2

Slant height of the pyramid = 6 cm

CONCEPT:

Area of slant surface of pyramid = Area of triangle

Pyramid will have 4 slant surfaces.

FORMULA USED:

Area of slant surface of pyramid = 1/2 × Base × Height

CALCULATION:

Let side of square base of the pyramid = ‘a’

Area of slant surface = (1/2) × 6 × a = 24

⇒ a = 8 cm

Total slant surface area of the pyramid = 4 × 24 = 96 cm2

Base area of the pyramid = 82 = 64 cm2

∴ Required ratio = 96: 64 = 3: 2

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