Area blue is;
Quarter the area of the square.
= ¼(10)²
= ¼(100)
= 25 cm²
Let the side of the two congruent sides be a units.
The small green square side will be;
⅔(a) units.
The big green square side is;
2a - ⅔(a)
= ⅓(4a) units.
b = a-⅔(a)
b = ⅓(a) unit...
Sir Mike Ambrose is the author of the question.
Shaded area exactly in cm² is;
Area triangle with height 84 cm and base 13 cm - Area triangle with height 10 cm and base 24 cm + Area triangle wi...
Radius of the circle, r is;
r² = (8+(3/2))²+4²
r² = (19/2)²+16
r² = ¼(425)
r = ½(5√(17)) cm
Therefore;
Area shaded, exactly in cm² decimal is;
Area sector with radius ½(5√(17)) cm an...
Calculating r, radius of the circle.
(r/tan40)+(r/tan30) = 10
r = 3.42020143326 cm.
(a/sin60) = (10/sin40)
a = 13.47296355334 cm.
tan40 = 3.42020143326/b
b = 4.07603734548
(4.076037...
Sir Mike Ambrose is the author of the question.
Let the small inscribed square side length be x.
The big inscribed square side length will be 2x.
Calculating x.
⅓(√(3)x+2√(3)x+3x+6x) = 18...
Notice;
AB = 25 units.
cos30 = 8√(3)/a
a = 16 units.
tan30 = b/(8√(3))
b = 8 units.
Let the side of the regular hexagon be c.
c = ¼(AC)
Calculating AC.
((AC)/sin46) = (25/sin74...
Calculating green inscribed triangle area.
a² = 2(3√(2))²
a² = 2*18
a = √(36)
a = 6 units.
a is AB.
b = ½(360-90)
b = ½(270)
b = 135°
b is angle ABC.
c² = 6²+(4√(2))²-2*6*4√(2)cos13...
Calculating the required angle, alpha.
Let it be a.
Let R = 2 units, radius of the ascribed semi circle.
b = (2-r) units.
It implies;
Calculating r.
(2-r)² = 2r²
2-r = √(2r²)
2-...
9^(x)+9*9^(x) = 270
Let 9^(x) be p.
p+9p = 270
10p = 270
p = 27
And p = 9^(x)
9^(x) = 27
2x = 3
x = 3/2
x = 1.5
