Answer to Question #148928 in Geometry for solid mensuration

Question

5. The total area of a regular tetrahedron is 110.85 m2, determine its base edge in m.

Answer 1

Solution. A regular tetrahedron consists of four regular triangles. Therefore, the total area of a regular tetrahedron is equal to

$$S_{total}=4\times\frac{1}{2}a^2sin60^0=a^2\sqrt{3}$$

where a is the edge of the regular tetrahedron. Аccording to the condition of the problem

$$S_{total}=110.85m^2$$

Hense

$$a^2\sqrt{3}=110.85$$ $$a=\sqrt{\frac{110.85}{\sqrt{3}}}\approx 8m$$

Answer. 8m