The area of a polygon is given by the formula Area = ap/2 where a is the length of the apothem and p is the perimeter. The apothem is a line from the center of the polygon perpendicular to a side.
Depending on the formula you know, you can find the length of a side in 1 of 2 ways.
The first way uses a triangle. Using the radius of the polygon you can create 8 congruent triangles. The center angle will be 360 / 8 = 45 and two side lengths of 20. You can find the length of the base using the law of cosines.
c^2 = 20^2 + 20^2 - 2(20)(20)(cos 45)
c^2 = 400 + 400 - 800(cos 45)
c^2 = 800 - 800(cos 45)
c = sqrt(800 - 800(cos 45)
c = 15.31
The second way is to use this formula:
r = s / (2 sin(180 / n))
20 = s / (2 sin(180/8)
(20)(2)sin(22.5) = s
(40)sin(22.5) = s
s = 15.31
We need to calculate the perimeter. As there are 8 sides (8)(15.31) = 122.48
Now we need to calculate the apothem using
a = S / (2 tan (180 / n)
a = 15.31 / (2 tan (180 / 8))
a = 18.48
Now solve for the area
Area = ap/2
Area = (18.48)(122.48)/2
Area = 1131.72
perimeter = 122.48
area = 1131.72
<h3>Answer :</h3>
<u>Given</u> :
- 9(m + 5) - 3(m - 2) = 8m + 31
We have to find value of m
➠ 9(m + 5) - 3(m - 2) = 8m + 31
➠ 9m + 45 - 3m + 6 = 8m + 31
➠ 9m - 3m + 45 + 6 = 8m + 31
➠ 6m + 51 = 8m + 31
➠ 51 - 31 = 8m - 6m
➠ 20 = 2m
➠ m = 20/2
➠<u> m = 10</u>
<h3>Hope It Helps!</h3>
The slope is (4,3). You look at the y intercept (where the y axis is crossed by the line) and simply count rise over run until you reach the next point. The next point from the y intercept (-2,0) is (2,3).
-2+4=2
0+3=3
And there you go. In fraction form it’s 4/3.
Hope this helped!
Q1. The answer is 4(2x - 3)(2x + 1)
16x² – 16x – 12 = 4 * 4x² - 4 * 4x - 4 * 3 =
= 4(4x² - 4x - 3) =
= 4(4x² + 2x - 6x - 3) =
= 4(2x * 2x + 2x - (2x * 3 + 3)) =
= 4(2x(2x + 1) - (3(2x + 1))) =
= 4((2x + 1)(2x - 3)) =
= 4(2x - 3)(2x + 1)
Q2. The answer is 3(x + 8)(x - 1)
3x² + 21x – 24 = 3 * x² + 3 * 7x - 3 * 8 =
= 3(x² + 7x - 8) =
= 3(x *x - x + 8x - 8) =
= 3((x(x - 1) + 8(x - 1)) =
= 3(x + 8)(x - 1)
