The base of the pyramid is a rhombus with diagonals of 10 and 18 cm. The height of the pyramid passes through

| February 18, 2021 | education

The base of the pyramid is a rhombus with diagonals of 10 and 18 cm. The height of the pyramid passes through the intersection of the diagonals of the rhombus. the smaller side edge of the pyramid is 13 cm. Find the larger side edge of the pyramid?

It is known that the diagonals of a rhombus are halved at the intersection point. If the height of the pyramid passes through the point of intersection of the diagonals, then the top of the pyramid is projected to this point, therefore, the side edges are projected on half of the diagonals of the base.

Knowing that the smaller side edge is 13 cm, half of the smaller diagonal is 10/2 = 5 cm, by the Pythagorean theorem we can find the height of the pyramid:

h ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144 = 122;

h = 12 cm.

Knowing the height of the pyramid and half of the larger diagonal 18/2 = 9 cm, we find the larger side edge:

l ^ 2 = 12 ^ 2 + 9 ^ 2 = 144 + 81 = 225 = 152;

l = 15 cm – larger lateral rib.



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