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

Explanation:

Step1: Calculate the base area

The base is a square with side length \(s = 40\) inches. The area of a square is \(A_{base}=s^{2}\). So, \(A_{base}=40^{2}=1600\) square inches.

Step2: Calculate the lateral surface area

The lateral surface area of a square - pyramid is \(A_{lateral}=4\times(\frac{1}{2}\times s\times l)\), where \(s = 40\) inches (base side length) and \(l = 29\) inches (slant height).

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Step3: Calculate the total surface area

The total surface area \(A = A_{base}+A_{lateral}\).

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Answer:

3,920 square inches