# On the side of the base d = 6 cm and the side edge b = 12 cm of a regular triangular prism

On the side of the base d = 6 cm and the side edge b = 12 cm of a regular triangular prism, determine the cross-sectional area of the edge and the axis of the prism drawn through the side-side.

Since the prism is based on an equilateral triangle, the axis of symmetry OO1 of the prism passes through the intersection points of the medians of the triangle, which are also heights and bisectors.

Then the required section is the rectangle CC1KH.

Determine the length of the segment CH. AC = 6 cm by condition, AH = AB / 2 = 6/2 = 3 cm, since CH is the median, then, according to the Pythagorean theorem, CH ^ 2 = AC ^ 2 – AH ^ 2 = 36 – 9 = 27.

CH = 3 * √3 cm.

Determine the cross-sectional area.

Ssection = CH * CC1 = 3 * √3 * 12 = 36 * √3 ≈ 62 cm2.

Answer: The cross-sectional area is ≈ 62 cm2.

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