The Tetrahedron Superyacht designed by Jonathan Schwinge is a regular tetrahedron with edges $$20 {~m} {long}$$. The distance $$r$$ from one corner to the center of the base (shown in the picture below) is $$11.5 {~m}$$. ![](http://admin.getprephub.com/media/editor/rt6_20230203221208174126.png) What is the vertical height $${h}$$ of the tetrahedron? Round your answer to the nearest tenth of a meter.

From the diagram, $$ r =11.5 {~m} , h =?$$ length of each edge $$(a)=20$$ m By pythagoream theorem, $$ r^{2}+h^{2}=20^{2} $$ $$\text { or, }(11.5)^{2}+h^{2}=400 $$ $$\text { or, } h^{2}=400-132.25=267.75 $$ $$h=16.4 \text { m}$$

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The Tetrahedron Superyacht designed by Jonathan Schwinge is a regular tetrahedron with edges $20 {~m} {long}$ . The distance $r$ from one corner to the center of the base (shown in the picture below) is $11.5 {~m}$ .

What is the vertical height ${h}$ of the tetrahedron?

Round your answer to the nearest tenth of a meter.

$16.4$

$17$

$18.2$

$19$

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