Let k = 1 unit.
a = 5+1
a= 6 units.
a is the side length of the square.
b = ½(a)
b = 3 units.
c = b-1
c = 2 units.
tand = 6/2
d = atan(3)°
e = (180-atan(3))°
It implies;
(...
Let the radius of the ascribed circle be 1 unit.
Therefore;
Area blue is;
12(area sector with radius 1 unit and angle 60° - area equilateral triangle with single side length 1 unit).
=...
Purple area is;
Area triangle with height 4 units and base 8 units - (area square with side 4 units - area quarter circle with radius 4 units) - area sector with radius 4 units and angle (180-2...
Sir Mike Ambrose is the author of the question.
Let the single side length of the congruent regular hexagons be 1 unit.
Therefore;
Area red is;
Area trapezium with two parallel side leng...
8² = (3+a)²+(5+a)²
Where a is the radius of the inscribed circle.
64 = 9+6a+a²+25+10a+a²
64 = 34+16a+2a²
a²+8a-15 = 0
(a+4)² = 15+16
a = -4±√(31)
It implies;
a = √(31)-4
a = 1.5677643628 u...
Let the side length of the ascribed regular hexagon be 2 units.
Calculating Area B.
½*1*1sin60
= ¼√(3) square units.
a = ⅙*180(6-2)
a = 120°
a is the single interior angle of the ascrib...
Notice.
ABCD is a square.
Let AB equal 1 unit.
sin70 = 1/a
a = 1.0641777725 units.
a is AE.
b = 90-70
b = 20°
b is angle DAE.
c = 90-45-20
c = 25°
c is angle BAF.
cos25 = 1/...
Let the radius of the quarter circle be a.
b = (a-4) units.
c = (a-2) units.
It implies;
a² = (a-4)²+(a-2)²
a² = a²-8a+16+a²-4a+4
a²-12a+20 = 0
a²-2a-10a+20 = 0
a(a-2)-10(a-2) = 0...
Sir Mike Ambrose is the author of the question.
Area red is;
Area triangle with height (18/7) units and base (24/7) units.
= ½((18/7)*(24/7))
= (216/49) square unit.
Area orange is;
Ar...
Sir Mike Ambrose is the author of the question.
Area purple is;
Area trapezium with two parallel side length (58/15) cm and (46/5) cm, and height 4 cm.
= ½((58/15)+(46/5))*4
= (392/15) cm²...
