Triangular pyramid

A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm

Correct answer:

h =  6.532 cm

Step-by-step explanation:

$$\begin{gathered} a=8\text{cm} \\ {a}^2=h_1^2+(a/2{)}^2 \\ {h}_1=\sqrt{a^2-(a/2{)}^2}=\sqrt{8^2-(8/2{)}^2}=4\sqrt{3}\text{cm}\doteq 6.9282\text{cm} \\ {h}^2+(2/3h_1{)}^2=a^2 \\ h=\sqrt{a^2-(2/3\cdot h_1{)}^2}=\sqrt{8^2-(2/3\cdot 6.9282{)}^2}=6.532\text{cm} \end{gathered}$$

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