Take a horizontal cross-section of the pyramid. Let be the smaller side of the cross-section and let be the height from the cross-section to the base of the pyramid. Due to similarity, the longer side of the cross-section must have length and the area will be . Therefore, the volume of the pyramid will be

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To find in terms of , use the similarity of triangles (vertically 'slice' the pyramid in half and examine the cross-section).