# In a regular triangular prism, the lengths of all edges are 2 cm.

In a regular triangular prism, the lengths of all edges are 2 cm. Find the area of the section drawn through the side edge and the middle of the opposite side of the base.

Points H and H1 are the midpoints of sides AB and A1B1 of equilateral triangles at the base of the prism. The height of CH is also the median of the triangle ABC, then AH = BH = AB / 2 = 2/2 = 1 cm.

In a right-angled triangle BCH, according to the Pythagorean theorem, CH ^ 2 = BC ^ 2 – BH ^ 2 = 4 – 1 = 3 cm.

CH = √3 cm.

The section of the prism is a rectangle CC1H1H, then Ssec = CC1 * CH = 2 * √3 cm2.

Answer: The cross-sectional area is 2 * √3 cm2.

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