Calculating shaded red area.
Let a be the diameter of the inscribed big half circle.
Therefore, 2a is the diameter of the bigger half circle or a is the radius of the bigger half circle.
a²...
a² = 4²+4²-2*4*4cos120
a² = 32+16
a² = 48
a = 4√(3) cm.
b²+(0.5a²) = 4²
b² = 16-12
b = √(4)
b = 2 cm.
Or
cos60 = b/4
½ = b/4
b = 2 cm.
Therefore, total surface area of the hexag...
Let a be the radius of the inscribed green circle.
tan30 = a/b
b = √(3)a cm.
c = ½(3√(3)-π) cm²
d = 60π*a²/360
d = ⅙(πa²) cm²
Therefore;
0.5*a*√(3)a = ½(3√(3)-π)+⅙(πa²)
½√(3)a² =...
Angle ABC = ½(angle BAC) since angle ACD and angle BCD are equal and length BC = length AD + length AC
It implies;
a +½(100)+100 = 180
a = 180-150
a = 30°
a is angle ACB.
b = ½(a)
b =...
Let AB = 1 unit.
a = 180-15-30
a = 135°
a is angle ADB.
(1/sin135) = (b/sin15)
b = 0.3660254038 units.
b is BD = CD.
c = 2b
c = 0.7320508076 units.
c is BC.
d² = 0.7320508076²+1²...
(9^(p)*81)-9^(p) = 240
Let 9^(p) = a.
81a-a = 240
80a = 240
a = 3
It implies;
9^(p) = 3
p = ½
Therefore;
(8p)^(p) is;
√(8*½)
= √(4)
= 2
a² = 6²+9²-2*6*9cos60
a = 7.9372539332 units.
(7.9372539332/sin60) = (6/sinb)
b = 40.8933946491°
(7.9372539332/sin120) = (6/sinc)
c = 40.8933946491°
d = c+b
d = 81.7867892983°
e = 1...
Calculating area of the ascribed square and area of the inscribed blue triangle.
a²+8² = 10²
a = 6 units.
6 - 8
b - x
Cross Multiply.
8b = 6x
b = ¼(3x) units
c²+x² = 8²
c = √(64...
Let AB be 1 unit.
a = 180-18-36
a = 126°
a is angle APB.
(1/sin126) = (b/sin18)
b = 0.3819660113 units
b is BP.
c = 180-(12+18)-(36+36)
c = 180-102
c = 78°
c is angle ACB.
(1/s...
Notice.
The complete plane shape is half a circle with radius 8 cm.
Area green is;
Area semi circle with radius 8cm - 2(area quarter circle with radius 8 cm - area triangle with height and...
