A₆ =12
a₇ = ?? = x
a₈ 27
In this case x is the geometric mean & as per the formula
geometric mean of 2 numbers =√(a₆ * a₈) = √(12*27)
& x=18.
Proof:
Find the common ratio between a₇ & a₆ ==> = ( x) / 12
now find the common ration between a₈ & a₇ ===> =27 / (x)
x/12 = 27/x ===> x² = 12*27 ==> x² = 324 & x =√324 = 18
Richelle can fold a hexagon in half and if they match up they will be congruent.
all angles would be congruent
The first would be “6x squared” and the 2nd term would be “5xy”
We have a bunch of rectangles making up the lateral sides of this figure. They have side length 12 and height 13.
So the area of one rectangle is 12 x 13 = 156.
We have 6 of these rectangles, so our lateral area is 6(156) = 936.
The total surface area requires that we include the area of the base. To find the area of a regular polygon we take half of the product of the apothem and perimeter.
A = (1/2)*a*p
The apothem is given to be 10.39,
and the perimeter is fairly easy to calculate:
With the side length being 12, the perimeter is then 6(12) = 72.
So then the area of our base is (1/2)*10.39*72 = 374.04
So then the total surface area is the (base area) + (lateral area),
374.04 + 936 = 1310.04
