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1. Find the volume of a pyramid with a rectangular base of dimensions 32 by 66 and with lateral edge 65.

2. The volume of a regular hexagonal pyramid, with base edge length half as long as the height, is 5123‾√5123. Find the lateral area of the pyramid.

Apr 18, 2019

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$$V = \dfrac{1}{3}Ah$$

$$A = 32 \cdot 66 = 2112$$

$$h = \sqrt{65^2-\left(\dfrac{32}{2}\right)^2-\left(\dfrac{66}{2}\right)^2} = 24\sqrt5$$

$$V = \dfrac{1}{3}(2112)(24\sqrt5) = 16896\sqrt5$$

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Apr 18, 2019