The base of the straight prism is a rhombus with an acute angle of 30 degrees, the diagonal of the lateral edge is 8 cm
| April 15, 2021 | education
The base of the straight prism is a rhombus with an acute angle of 30 degrees, the diagonal of the lateral edge is 8 cm and forms an angle of 60 degrees with the base plane. Find the total area of the prism.
In a right-angled triangle АА1D, the angle АА1D = (90 – АDА1) = (90 – 60) = 30.
Leg AD is erect opposite angle 30, then its length is equal to half the length of hypotenuse A1D.
AD = A1D / 2 = 8/2 = 4 cm.
Then АА1 ^ 2 = А1D ^ 2 – АD ^ 2 = 64 – 16 = 48.
AA1 = 4 * √3 cm.
Determine the area of the base of the prism.
Sbn = AB * AD * Sin30 = 4 * 4 * 1/2 = 8 cm2.
Determine the total area of the prism.
Spov = 2 * Sb + S side = 2 * Sb + Ravsd * AA1 = 2 * 8 + 16 * 4 * √3 = 16 * (1 + 4 * √3) cm2.
Answer: The total surface area is 16 * (1 + 4 * √3) cm2.
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