The base of the straight prism is a rhombus with diagonals equal to 9 and 12, and a side edge equal to 6.
| February 7, 2021 | education
The base of the straight prism is a rhombus with diagonals equal to 9 and 12, and a side edge equal to 6. Find S of the prism surface.
Determine the area of the base of the prism.
Sbn = AC * ВD / 2 = 12 * 9/2 = 54 cm2.
The diagonals of the rhombus, at the point of their intersection, are divided in half and intersect at right angles, then ОВ = BD / 2 = 9/2 = 4.5 cm, ОА = АС / 2 = 12/2 = 6 cm.
By the Pythagorean theorem, AB ^ 2 = OA6^2 + OB6^2 = 36 + 20.25 = 56.25.
AB = 7.5 cm.
Determine the total surface area of the prism.
Spov = 2 * Sb + S side = 2 * Sb + P * AA1 = 2 * 54 + 4 * 7.5 * 6 = 288 cm2.
Answer: The total surface area is 288 cm2.
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