a = ½(5+35)
a = 20 units.
a is the radius of the ascribed semi circle.
b = (20-c) units.
d = a-5
d = 20-5
d = 15 units.
Therefore;
(20-c)² = c²+15²
400-40c+c² = c²+225
175 = 40c...
Sir Mike Ambrose is the author of the question.
Let the big square area be 4 square units.
Therefore the bigger square area will be;
16 square units.
Area blue is;
Area square with lengt...
3² = a²+2²
a² = 9-4
a = √(5) units.
a is PQ.
cosb = 2/3
b = acos(2/3)°
b is angle BAC.
tan(acos(2/3)) = (5√(5))/c
c = 10 units.
c is AB.
d = 10-3
d = 7 units.
d is PB.
e² = 7²+...
a = (x+60)°
b = (180-7x)°
Notice.
Blue triangle is equilateral.
Yellow triangle is isosceles.
L1 is parallel to L2
Therefore;
a = b
(x+60) = (180-7x)
8x = 120
2x = 30
x = 1...
Sir Mike Ambrose is the author of the question.
Area green, exactly is;
Area square with length 8 cm - area trapezoid with two parallel length 8 cm and 2 cm, and height 3 cm - area trapezoid wi...
Calculating area inscribed yellow rectangle.
tana = 20/15
a = atan(4/3)
b = 90+a
b = (90+atan(4/3))°
(20/sin(90+atan(4/3))) = (15/sinc)
c = 26.7436839504°
d = 180-(90+atan(4/3))-26.7...
1. The Right-angled Triangle.
Calculating length x.
a = 9+6
a = 15 cm.
a is the height of the ascribed right-angled triangle.
17 cm is the hypotenuse of the ascribed right-angled triangl...
Let the radius of the quarter circle be a.
b = 2a units.
c = 4+5
c = 9 units.
It implies;
3²+9² = (2a)²
4a² = 90
a² = ½(45)
a = ½(3√(10)) units.
a = 4.7434164903 units.
Again, a i...
Let a be the radius of the circle.
tanb = (0.5a)/a
b = atan(0.5)°
cos(atan(0.5)) = c/6
c = 5.366563146 units.
sin(atan(0.5)) = d/6
d = 2.683281573 units.
cosatan(0.5) = 3/a
a = 3.35...
Calculating r, radius of the quarter circle
Notice.
AE = DE = 1 unit.
CE = 6+1
CE = 7 units.
AC = √(2r²)
AC = √(2)r units.
It implies;
(√(2)r)² = 7²+1²
2r² = 50
r = √(25)
r...
