Calculating Area Blue Circle.Notice.10 units is the side length of the square.a = (10+2x) units.b = ½(a)b = ½(10+2x)b = (5+x) units.b is the radius of the blue circle.c = b-2xc = 5+x-2xc = (5-x) unit...
Calculating perimeter of the blue inscribed square.5² = 7²+8²-2*7*8cosa112cosa = 49+64-25cosa = 88/112a = acos(11/14)a = 38.2132107017°5/sin38.2132107017 = 7/sinbsinb = ⅕(7sin38.2132107017)sinb = 0.8...
Calculating r, radius of the circle.Let the small inscribed right-angled triangle shortest length be x.3 ~ 4x ~ aCross Multiply.3a = 4xa = ⅓(4x) units.a is the big inscribed right-angled triangle sho...
Calculating x.a² = 9a = √(9)a = 3 units.a is the side length of the inscribed square.b² = 3²+3²b² = 2*3²b = √(2*3²)b = 3√(2) units.b is the radius of the half circle.c = 2bc = 2*3√(2)c = 6√(2) units....
Calculating R, radius of the blue circle.a = (R-2) cm.b = ½(20)b = 10 cm.R, radius of the blue circle is;R² = (R-2)²+10²R² = R²-4R+4+1004R = 104R = 26 cm.
Calculating Area Red.Let x be the radius of the circle.a = (x-7) cm.Calculating x.x²+(x-7) = 13²x²+x²-14x+49 = 1692x²-14x-120 = 0x²-7x-60 = 0x²-12x+5x-60 = 0x(x-12)+5(x-12) = 0(x-12)(x+5) = 0It impli...
Sir Mike Ambrose is the author of the question.Calculating Area Blue ÷ Area Green to 2 decimal places.Let the side length of the regular pentagon be 1 unit.tan36 = a/0.5a = 0.363271264 unit.b² = 0.36...
Area shaded in pink (area A) is;Notice:The single side length of the square is;3√(2) units.Shaded yellow area height is;Height = 6/(3√(2))= √(2) units.Therefore area A is;Height = 3√(2)-√(2) = 2√(2)...
Calculating x.Notice.The ascribed irregular quadrilateral is cut out a regular triangle (Equilateral Triangle).Therefore, resolving with the above fact/analysis.a = (x+6) units.a is the side length o...
Calculating the required red length.Let a be the radius of the half circle.b = (a-1) units.c²+1² = b²c² = a²-2a+1-1c = √(a²-2a) units.d = a+c d = (a+√(a²-2a)) units.d is the required length.e = (a+1...
