Aregular hexagon has an apothem of 14.7 inches and a perimeter of 101.8 inches. what is the area of the hexagon?

Answer

748.23 in²

Explanation

Apothem a line from the centre of a regular polygon at right angles to any of its sides. This can be said to be the height of the triangle in a polygon.

The base of the  hexagon = 101.8 ÷ 6

                                            = 19.96666..

                                            = 19.9667 inches

Area of the  hexagon = 1/2 × height × base length × 6

                                     = 1/2 × 14.7 × 19.9667 × 6

                                      = 748.23 in²

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560