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...
Calculating angle x.
Let the radius of the inscribed half circle be 1 unit.
Therefore, 2 units is the radius of the ascribed quarter circle.
a = (2-y) units.
b² = 1²+y²
b = √(1+y²) unit...
The Great Graph Gala.
Barnaby Bear loved berries. Big berries, little berries, red berries, blue berries - he loved them all!
He especially loved sharing them with his friends. There was Ferdinan...
Calculating a.
tan60 = a/b
√(3) = a/b
b = a/√(3)
b = ⅓(√(3)a) units.
tan60 = 2a/c
√(3) = 2a/c
c = 2a/√(3)
c = ⅓(2√(3)a) units.
It implies;
b+a+2a+c = 1
⅓(√(3)a)+a+2a+⅓(2√(3)a)...
Calculating x, the required angle.
a = ⅛*180(8-2)
a = ⅛*180*6
a = ½*45*6
a = 135°
a is the single interior angle of the regular octagon.
b = ⅕*180(5-2)
b = ⅕*180*3
b = 36*3
b = 108°
b...
