At the base of a straight prism lies a rhombus with diagonals of 18 and 24 cm. Determine the height of the prism if its lateral surface area is 225 cm2.
The diagonals of the rhombus lying at the base of the prism are divided in half at the point of intersection and intersect at right angles, then A1O = A1C1 / 2 = 24/2 = 12 cm, B1O = B1D1 / 2 = 18/2 = 9 cm.
Then in a right-angled triangle A1B1O, A1B1 ^ 2 = A1O ^ 2 + B1O ^ 2 = 144 + 81 = 225.
A1B1 = 15 cm.
Determine the perimeter of the base of the prism. Since all sides of a rhombus are equal, then Rosn = 4 * A1B1 = 4 * 15 = 60 cm.
Determine the heights of the prism.
Sside = АА1 * Rusn.
AA1 = S side / Rosn = 225/60 = 3.75 cm.
Answer: The side edge of the prism is 3.75 cm.
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