Grades 11-12 Video Solutions 2026-2026_11-12

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Question 18. This hexagonal prism has 2 regular hexagons and 6 squares as faces. All edges are 1 unit long. What is the length of the line segment AB shown? a, square root of 2, b, square root of 3, c, square root of 4, d, square root of 5, or e, square root of 6. Let us label the point right above B as C and draw a line between A and C. Now, we split the top hexagon into 6 equilateral triangles. Notice how AC is equal to 2 times the height of these equilateral triangles. These triangles have a side length of 1, which means that these triangles have a height of square root of 3 over 2, so AC has a length of square root 3. Since angle ACB is a right angle, we can now use the Pythagorean theorem to find that AB is equal to the square root of the square root of 3 squared plus 1 squared, which is equal to the square root of 4, or answer choice C.

Keywords

hexagonal prism

regular hexagon

Pythagorean theorem

equilateral triangles

square root of 4