# Find the area of the smaller diagonal section of a regular hexagonal prism if all of its edges are 6.

March 31, 2021 | education

| Regular hexagonal prism – at the base a regular hexagon, side faces – rectangles.

The area of its smaller diagonal section is equal to the product of the height 6 and the base of an isosceles triangle with sides 6.

Let’s find the angle between its lateral sides as the angle of a regular hexagon:

180 ° * (6 – 2): 6 = 120 °.

The height dropped from this angle to the base divides it in half, and so does the angle.

Find the length of the base of this triangle using the ratio of the angles of a right-angled triangle.

a / 6 = sin60 ° = √3 / 2.

a = √3 * 6/2 = 3√3.

3√3 * 2 = 6√3 – base length.

Let’s find the area of the small diagonal section of the prism.

S = 6√3 * 6 = 36√3.

Answer: S = 36√3.

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