Calculating the ascribed square area.
Let x be the square side length.
a = 6+7
a = 13 units.
b²+x² = 13²
b = √(169-x²) units.
Calculating x², area of the ascribed square..
√(169-x²...
Calculating Area Yellow.
a = (3+x) units.
a is the width of the ascribed rectangle.
b = 2(7)
b = 14 units.
b is the length of the ascribed rectangle.
c = ½(a)
c = ½(3+x) units.
tany...
Calculating Length x.
Let Alpha be y.
Again.
Let AB = a.
b = 2+6
b = 8 units.
tany = a/8 --- (1).
tany = 2/a --- (2).
Equating (1) and (2).
(a/8) = (2/a)
Cross Multiply....
Leonhard Euler (1707- 1783)
The most prolific mathematician of all time, publishing close to 900 books. When he went blind in his late 50s his productivity in many areas increased. His famous form...
Calculating Area Blue.
Let x be CE = CD = DE.
y = 6+4
y = 10 cm.
y is AC.
Observing Similar Plane Shape Rule.
10 ~ x
x ~ 4
Cross Multiply.
x² = 40
x = √(40)
x = 2√(10) cm.
Again...
Calculating Area Yellow.
Let a be the radius of the ascribed quarter circle.
(2a)² = b²+24²
b = √(4a²-576) units.
c = b-7
c = (√(4a²-576)-7) units.
It implies;
Calculating a.
(√...
Benny's Button Bonanza.
Benny lived in a bouncy house. Not really, but it felt like it! His dad was a bouncy house blower-upper, which is a very bouncy job indeed. One day, Benny’s dad said, “Let’...
Calculate x²+y².
Notice.
1 unit is the radius of the circle.
a = (y-x) units.
2b² = a²
2b² = (y-x)²
2b² = y²-2xy+x²
b² = ½(y²-2xy+x²)
b = √(½(y²-2xy+x²)) units.
c = 1-b
c = (1-...
Calculating Length x.
cosa = 40/50
a = acos(⅘)°
b = 2a
b = 2acos(⅘)°
Therefore, the required length x is;
cosb = x/50
cos(2acos(⅘)) = x/50
x = 50cos(2acos(⅘))
x = 50*(7/25)
x = 2*...
Calculate Area Green.
Green Area is;
Area square with length 4 units - Area quarter circle with radius 2 units - Area square with length 2 units - 3(Area square with length 1 unit) - Area squ...
