18 - 2,3,6,8
24 - 2,4,6,8,12
HCF = 8
A regular decagon has 10 equal sides. An apothem is a perpendicular bisector to the side. This means 2 equal right triangle are formed on each side (20 equal right triangles) or 10 equal isosceles triangles.
Using the 10 equal isosceles triangles and A = .5(base)(height)
Base is a side and height is apothem
Area of regular decagon = 10 × .5 × 8 × 12.3 = 492.0 yd²
Answer: 492.0 yd²
Here's an example...
So, in our last example...
In the point ( -2, -1 ), x1 = -2 and y1 = -1 ... and, in the point ( 4, 3 ), x2 = 3 and y2 = 3
m = ( y2 - y1 ) / ( x2 - x1 ) = ( 3 - ( -1 ) ) / ( 4 - ( -2 ) ) = 4 / 6 = 2 / 3
But, notice something cool...
The order of the points doesn't matter! Let's switch them and see what we get:
In the point ( 4, 3 ), x1 = 4 and y1 = 3 ... and, in the point ( -2, -1 ), x2 = -2 and y2 = -1
m = ( y2 - y1 ) / ( x2 - x1 ) = ( -1 - 3 ) / ( -2 - 4 ) = -4 / -6 = 2 / 3 ... Same thing!
Let's try our new formula with the second example in the last lesson:
It was a line passing through
( -1, 4 ) and ( 2, -2 )
m = ( y2 - y1 ) / ( x2 - x1 ) = ( -2 - 4 ) / ( 2 - ( -1 ) ) = -6 / 3 = -2
1) x + 3.2= -3.5
subtract 3.2 from both sides
x+ 3.2 - 3.2= -3.5 - 3.2
it cancels out on the left
x= -6.7
2) 8/9x= 32
divide both sides by 8/9
8/9x ÷ 8/9= 32 ÷ 8/9
it cancels out on the left
to divide on the right, multiply fraction by its reciprocal/inverse
x= 32 * 9/8
multiply numerators (top)
x= (32*9)/8
x= 288/8
x= 36
ANSWER: 1) x= -6.7; 2) x= 36
Hope this helps! :)
