Answer:
384√3 in²
Step-by-step explanation:
Given in the question a regular 6 sided polygon
To find it's area you have to use the following formula
<h3> 1/2 x perimeter x apothem</h3>
<em>Perimeter = the sum of the lengths of all the sides </em>
<em>Suppose length of one side = x</em>
<em>Apothem = a segment that joins the polygon's centre to the midpoint of any side that is perpendicular to that side = 8√3</em>
<em />
Since the polygon have 6 sides so
perimeter = 6x
<h3>x = 2(8√3)/√3</h3>
x = 2(8)
x = 16
perimeter = 6(16) = 96 in
plug values in the formula of area
<h3>1/2 x 96 x 8√3</h3>
384√3 in²
And because we know that we cut the base of the equilateral triangle in half, we can see that the side opposite the 30° angle (the shortest side) of each of our 30-60-90 triangles is exactly half the length of the hypotenuse.
A. when subtracting fractions with the same denominator, simply subtract the numerators and keep that number over the original denominator. Thus 11/12-7/12 becomes 4/12. But, this answer is not reduced because 4 is a factor of both the numerator and the denominator. Thus, divide 4 by 4 and 12 by 4 to get the new numerator and denominator. Your final fraction is 1/3.
b. In this expression, the fractions do not all have the same denominator, so you cannot subtract them yet. Your largest denominator is 8 but not all the other denominators are factors of 8. So to make a common denominator with all the fractions, you need to find a number that all the denominators are factors of. One example in this case is 24. Each of these fractions must then be expressed in terms of this common denominator. To do this, you need to find what can be multiplied by the original denominator to make 24. In other words, divide 24 by the original denominator and multiply that answer by the original numerator. In the case of 1/2, 24/2 is 12 and 12 x 1 is 12. Thus, the new fraction is 12/24. The second fraction is also done this way: 24/8=3 and 3x1 is 3 so the new fraction is 324. The third fraction should be handled the same way: 24/4 is 6 and 6x3 is 18 so the new fraction is 18/24. Finally, in 1/6, 24/6 is 4 and 4x1 is 4 so the new fraction is 4/24. Then, like the previous problem, when you perform 12/24 + 3/24 + 18/24-4/24= 29/24. Since 29 is larger than 24, this should be reduced. Do this by subtracting the denominator from the numerator and keep the remaining fraction. The final answer is 1 and 5/24.
51% less.
The length is decreased by 50%, which is the same as being multiplied by 0.5, then it's increased by 40% which is another multiplication by 1.4. So the overall change is 0.5 * 1.4 = 0.7, or the newest rectangle is 70% of the size of the original rectangle. And since the area increases by the square, the newest rectangle has 0.7 * 0.7 = 0.49 of the area as the original rectangle. So it has 51% less area than the original rectangle.
Answer: x = 28
Step-by-step explanation:
x + 20=3x-36
20=2x-36
56=2x
56/2=28
So 28= x
