(x-2) + (x-1) + x + (x+1) + (x-2) + (x+3) = 447
6x + 3 = 447
6x = 447 - 3
6x = 444
x = 444/6
x = 74
We know that
if two lines are perpendicular
then
the slopes
m1*m2=-1
step 1
find the slope AB
A (0,2)
B (-3,-3)
m=(y2-y1)/(x2-x1)-----> m=(-3-2)/(-3-0)-----> m=-5/-3----> m1=5/3
step 2
find the slope CD
C (-4,1)
D (0,-2)
m=(y2-y1)/(x2-x1)-----> m=(-2-1)/(0+4)-----> m=--3/4----> m2=-3/4
step 3
multiply mi*m2
(5/3)*(-3/4)-----> -15/12
so
15/12 is not -1
therefore
AB is not perpendicular to CD
Area of square = 24cm²
⇒ Length = √24
Find the diagonal of half the square:
a² + b² = c²
c² = (0.5√24)² + (√24)²
c² = 6 + 24
c² = 30
c = √30
The diagonal of half of the square is the radius of the circle.
⇒ radius = √30
Area of the semicircle = 1/2πr² = 1/2π(√30)² =15π
Answer: 15π²
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