Answer:
A and D
Step-by-step explanation:
Since tangent is opposite/adjacent,
Tan 40 in this case would be x/3.8 (i used x because we don't know what the value is)
So, you set it up as an algebra problem
Tan40 = x/3.8
Multiply both sides by 3.8
3.8tan40 = x, Option A
And then, angle E is 50 degrees
So tan 50 = 3.8/x
Multiply both sides by x
tan50x = 3.8
Divide both sides by tan50
x= 3.8/tan50
So, A and D are both correct
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
