The pyramid is composed of a square base of area 16 and four isoceles triangles,in which each base angle measures 60 degree.What is the volume of the pyramid?

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{As} \mathrm{base} \mathrm{angle} \mathrm{of} \mathrm{isosceles} \mathrm{triangle} \mathrm{is} 60°, \mathrm{hence} \mathrm{third} \mathrm{angle} \mathrm{will} \mathrm{also} \\ \mathrm{be} 60°, \mathrm{hence} \mathrm{triangle} \mathrm{will} \mathrm{be} \mathrm{equilateral}. \\ \mathrm{We} \mathrm{know} \mathrm{that} \\ \mathrm{Volume} \mathrm{of} \mathrm{pyramid}=\frac{1}{3}{\mathrm{a}}^2\mathrm{h} \\ \mathrm{where} \mathrm{a} \mathrm{is} \mathrm{length} \mathrm{of} \mathrm{base} \mathrm{and} \mathrm{h} \mathrm{is} \mathrm{height} \mathrm{of} \mathrm{pyramid} \mathrm{and} \mathrm{h}=\frac{\mathrm{a}}{\sqrt{2}} \\ \mathrm{V}=\frac{1}{3}{\mathrm{a}}^2.\frac{\mathrm{a}}{\sqrt{2}}=\frac{{\mathrm{a}}^3}{3\sqrt{2}} \\ \mathrm{No} \\ \mathrm{Area} \mathrm{of} \mathrm{square} \mathrm{base}=16 \\ \Rightarrow {\mathrm{a}}^2=16 \\ \Rightarrow \mathrm{a}=4 \\ \mathrm{V}=\frac{4^3}{3\sqrt{2}}=\frac{64}{3\sqrt{2}}=\frac{32\sqrt{2}}{3} {\mathrm{unit}}^3 \end{gathered}$$

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