# In a straight triangular prism, the sides of the base are 25 dm, 29 dm and 36 dm, and the total surface is 1620 dm2.

In a straight triangular prism, the sides of the base are 25 dm, 29 dm and 36 dm, and the total surface is 1620 dm2. Determine the side surface and height of the prism.

1. Let:

a = 25 dm;
b = 29 dm;
c = 36 dm;
S = 1620 dm ^ 2;
h is the height of the prism.
2. The area of the base is found by Heron’s formula:

p = (a + b + c) / 2 = (25 + 29 + 36) / 2 = (25 + 29 + 36) / 2 = 45;
p – a = 45 – 25 = 20;
p – b = 45 – 29 = 16;
p – c = 45 – 36 = 9;
Sosn. = √ (p (p – a) (p – b) (p – c));
Sosn. = √ (45 * 20 * 16 * 9) = 30 * 4 * 3 = 360.
3. Side surface:

S = 2Sn. + S side .;
S side. = S – 2Sn. = 1620 – 2 * 360 = 1620 – 720 = 900.
4. Prism height:

S side. = Ph;

h = S side. / P = 900/90 = 10.

Answer: S side. = 900 dm ^ 2; h = 10 dm.

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