ABCD-is-a-rectangle-such-that-AD-2AB-and-its-center-is-O-H-is-the-top-of-a-pyramid-which-has-ABCD-as-base-All-lateral-faces-are-isosceles-triangles-planes-HAB-and-HCD-are-i-have-joined-a-g

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Question Number 139419 by mathocean1 last updated on 26/Apr/21

$$ABCDisarectanglesuchthat$$$$AD=2ABanditscenterisO.$$$$Histhetopofapyramidwhich$$$$hasABCDasbase.Alllateral$$$$facesareisoscelestriangles.planes$$$$\left(HAB\right)and\left(HCD\right)are\mathrm{\perp }.$$$$ihavejoinedagraphic.$$$$1.showthat\left(OH\right)\mathrm{\perp }\left(ABC\right).$$$$2.showthatOH=\frac{\sqrt{3}}{2}AB$$$$$$

Commented by mathocean1 last updated on 26/Apr/21

Commented by mr W last updated on 26/Apr/21

$$OH=AB\ne \frac{\sqrt{3}}{2}AB$$

Commented by mr W last updated on 27/Apr/21

Commented by mr W last updated on 27/Apr/21

Commented by mr W last updated on 27/Apr/21

$$HE\mathrm{\perp }HF$$$$OH=\frac{EF}{2}=\frac{AD}{2}=AB$$

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