Volume of a Square Pyramid: Base Perimeter and Height Calculation

Published on February 27, 2026

Geometry

Calculate the volume of a square-based pyramid given the perimeter of the base and the height. The solution involves finding the side length and area of the base, then applying the pyramid volume formula and rounding to the nearest tenth.

Question

Find the volume of a pyramid with a square base, where the perimeter of the base is 5, in5 in and the height of the pyramid is 3, point, 6, in3.6 in. Round your answer to the nearest tenth of a cubic inch

Answer

Here’s how to solve the problem step-by-step:

Find the side length of the square base:
The perimeter of a square is , where is the side length. We are given the perimeter is 5 in. So,

in
Find the area of the square base:
The area of a square is . So,
Area square inches
Find the volume of the pyramid:
The volume of a pyramid is , where is the area of the base and is the height. We have square inches and inches. So,
Volume cubic inches
Round to the nearest tenth:
rounded to the nearest tenth is .

Final Answer: The final answer is

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