Triangular prism

Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.

Correct result:

V =  65.45 cm3

Solution:

$a = 6 \ cm \ \\ h_1 = \dfrac{ \sqrt3}{2} a = 5.196 \ cm \ \\ \ \\ \tan 22 ^\circ = \dfrac{h/2}{h_1} \ \\ h = 2 h_1 \tan 22 ^\circ = 2 \cdot 5.196 \cdot \tan 22 ^\circ = 4.199 \ cm \ \\ S_1 = \dfrac12 a h_1 = \dfrac12 6 \cdot 5.196 = 15.588 \ cm^2 \ \\ V = S_1 h = 15.588 \cdot 4.199 = 65.45 \ \text{cm}^3 \ \\$

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