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The base of a right pyramid is a square and the length of the side of square is 32 cm and height of the pyramid is 12 cm, then what is the total surface area of the square pyramid?

The base of a right pyramid is a square and the length of the side of square is 32 cm and height of the pyramid is 12 cm, then what is the total surface area of the square pyramid? Correct Answer 2304 sq. cm

Given:

Base of a right pyramid is a square and the length of the side of square is 32 cm

Height of the pyramid is 12 cm

Formula used:

Total surface area = Lateral surface area + Area of the base

Lateral surface area = 1/2 × Perimeter of base × slant height

Calculation:

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In ΔOAB

The slant height, l

⇒ l2 = h2 + AB2

⇒ l2 = (12)2 + (16)2

⇒ l2 = 400

⇒ l = 20 cm

Now, Total surface area = Lateral surface area + Area of the base

⇒ 1/2 × Perimeter of base × slant height + Area of the base

⇒ 1/2 × (4 × 32) × 20 + (32)2

⇒ 1280 + 1024

⇒ 2304 sq. cm

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