Question

A square pyramid has a base with side lengths each measuring 40 inches. The pyramid is 21 inches tall, with a slant height of 29 inches. What is the surface area of the pyramid? 3,280 inches 3,280 square inches 3,920 inches 3,920 square inches

Answer 1

Answer    

Find out the  what is the surface area of the pyramid .

To proof

Formula

Surface area of a square pyramid

$= a^{2} + 2a \sqrt{\frac{a^{2}}{4} +h^{2}$

Where a is the base edge and h be the height .

As given

A square pyramid has a base with side lengths each measuring 40 inches. The pyramid is 21 inches tall, with a slant height of 29 inches.

i.e Base edge = 40 inches

Height =  21 inches    

Put values in the above formula

$= 40^{2} + 2\times40\times\sqrt{\frac{40^{2}}{4} +21^{2}$

solving

$= 1600 + 80 \sqrt{\frac{1600}{4} + 441$

$= 1600 + 80\times\sqrt{841}$

$\sqrt{841} = 29$

= 1600 + 80 × 29

= 3920 inches²

Therefore the surface area of the pyramid is 3,920 inches²

Hence proved

Answer 2

The surface area of the square pyramid is: 3920 sq. in.

Surface Area of Square Pyramid

• Surface area = a² + 2a × √(a²/4 + h²)
• a = side length; h = height

Given:

• a = 40 inches
• h = 21 inches

Thus:

Surface area of pyramid = 40² + 2(40) × √(40²/4 + 21²)

Surface area of pyramid = 3920 square inches.

Therefore, the surface area of the square pyramid is: 3920 sq. in.

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