“Mathematics is the most beautiful and most powerful creation of the human spirit.”

Stefan Banach

“To not know math is a severe limitation to understanding the world.” Richard Feynman

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“The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.”

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OnlineEdumath

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We mentor/educate/teach learners Mathematics online via Google Meet App. Our Certified, Resilient and Productive Mathematics Educators make teaching and learning Mathematics fun for learners. Communicate us to mentor your child/children to become a lover of Mathematics, and a Mathematician

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We are smart and clever!

By OnlineEdumath | 5th November, 2024

“Mathematics is the most beautiful and most powerful creation of the human spirit.” Stefan Banach

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Welcome to Online Edumath

By OnlineEdumath | 4th September, 2024

This is Online Edumath website created by Ogheneovo Daniel Ephivbotor. Online Edumath falls in EDUCATION line of business. You can visit us offline at our office located at : Lugbe, Federal...

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By OnlineEdumath | 3rd July, 2024

For enquiry on what we do and on our shared Mathematics Questions and Solution review, please communicate us via our WhatsApp contact: +2349076614992 We are kindly to respond to your question(s)/...

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By OnlineEdumath | 18th April, 2024

The Management and Educators of Online Edumath kindly appreciate your words of affirmation and encouragement, Sir Bill. We are grateful! We pledge to keep working hard as we mentor/educate our lea...

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By OnlineEdumath | 18th April, 2024

Online Edumath Educators and Learners are Super Smart and Amazingly, Very Clever. Communicate us to mentor/teach/educate your child/children Mathematics online at affordable tuition, helping them be...

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Mr. Daniel (Mathematics Educator)

By OnlineEdumath | 26th August, 2023

Mr. Daniel is one of our Educators, He is a certified, hardworking, dedicated and passionate Mathematics Educator that aim at taking the sincere, profound knowledge of Mathematics to the comfort of...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 30th June, 2025

Calculating shaded area. tana = 5/10 a = atan(½)° Therefore; b = atan(2)° c = 90-2a c = 90-2atan(½) c = 36.8698976458° d = 180-2b d = 180-2atan(2) d = 53.1301023542° Shaded A...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 30th June, 2025

Calculating x. a = 2*120 a = 240° b = 360-a b = 120° c = ½(180-120) c = 30° d = 2*140 d = 280° e = 360-d e = 80° f = ½(180-80) f = 50° It implies; x = c+f x = 30+50 x = 80°

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 30th June, 2025

Notice. r is the radius of the inscribed yellow half circle. r = ½(10) r = 5 units. Calculating R, radius of the ascribed circle. Calculating R. a = x+10+5 a = (x+15) units. b = ½(a) b = ½(x+1...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 30th June, 2025

Kindly move the question right or left one time to review the solution and answer. Solution and answer by Mehmet Kara. Thank you nicely.

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 29th June, 2025

Let AC = BD = DE = a. Calculating a. 14² = a²+(10+a)²-2a(10+a)cosb 96 = 2a²+20a-(20a+2a²)cosb --- (1). 14² = a²+10²+2a*10cosb 96 = a²+20acosb cosb = (96-a²)/(20a) --- (2). Substituting (2) in (1...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 29th June, 2025

Calculating Purple Area. tanb = 2/1 b = atan(2)° tanc = ½ c = atan(½)° d = 180-b d = (180-atan(2))° e = 180-d-c e = 180-(180-atan(2))-atan(½) e = (atan(2)-atan(½))° It implies; (1/sin(atan(2)-...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 29th June, 2025

Let 1 unit be the side length of the green square. Therefore; EN = ½ units. a = (1+2x) units. a is the diameter of the bigger circle. b = ½(a) b = ½(1+2x) units. b is the radius of the...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 28th June, 2025

R ~ (a+b) r ~ a Cross Multiply. aR = r(a+b) R/r = (a+b)/a R/r = 1+(b/a) And R/r = phi (golden ratio) Let phi be x. x-1 = b/a a/b = 1/(x-1) Where x (phi) is; x = ½(1+√(5))...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 28th June, 2025

Calculating Area A Divided By Area B (A/B). Let a be the two equal lengths. b = (3-a) units. c² = 4²+3² c = 5 units. Therefore; Calculating a. 5 ~ (3-a) 4 ~ a Cross Multiply. 5x = 12-4a 9a = 1...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 28th June, 2025

Let DC = 1 unit. a = 180-36+30 a = 114° a is angle BDC. (1/sin36) = (b/sin114) b = 1.55421636402 units. b is BC. c = 180-60-54 c = 180-114 c = 66° c is angle BAC. Therefore; (1.55421636402/sin6...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 28th June, 2025

Calculating R. 3R+4R+5R = 3*4 12R = 12 R = 1 units. Calculating r. tana = 3/4 a = atan(3/4)° b = ½(a) b = ½(atan(3/4))° tan(½(atan(3/4))) = r/c c = 3r units. d = 4-1-3r d = (3-3r) units. e...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 27th June, 2025

Let the height and base of the brown area be x and y respectively. Therefore; ½(3+x)(4+y)-42 = ½(xy) 12+3y+4x+xy-84 = xy 3y+4x = 72 --- (1). 3 ~ (3+x) 4 ~ (y+4) Cross Multiply. 4(...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 27th June, 2025

a² = 2(1)² a = √(2) units. a is the diagonal of the inscribed square and also the side length of the two congruent inside bigger regular triangle. b = ½(a) b = ½√(2) units. c²+b² = a² c² = √(2)²-...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 27th June, 2025

a = 2(20) a = 40 units. b = 60+20 b = 80 units. c = 2(20) c = 40 units. d = atan(80/40)+atan(20/40) d = 90° d is angle ACB Area Triangle ABC is; ½*√(80²+40²)*√(40²+20²) = ½*√(6400+1600)*√(1600...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 27th June, 2025

Let the inscribed green square side length be a. 2b² = a² b = ½√(2)a units. c² = 2(4)² c = 4√(2) units. c is the diagonal of the ascribed bigger square. It implies; 4+a+½(a) = c...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 26th June, 2025

Calculating x, length AD. c² = x²+3² c = √(x²+9) units. c is AC. d²+2² = c² d² = √(x²+9)²-4 d² = x²+5 d = √(x²+5) units. d is AB. Notice. a-b = 30 Therefore; a = (30+b)° sinb = x/√(x²+9) --- (1...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 26th June, 2025

Let b = 1 unit. Calculating a. c² = 2a² c = √(2)a units. c is the diagonal of each of the three identical squares. d = c-a d = (√(2)a-a) units. It implies; 1² = a²+(√(2)a-a)²-2a(√(2)a-a)cos45...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 26th June, 2025

Let the single side length of the square be (x+12) units. Calculating x. 18²=(x+12)²+(x+6)² 324=x²+24x+144+x²+12x+36 324=2x²+36x+180 2x²+36x-144=0 x²+18x-72=0 (x+9)²=72+81 x = -9±√(153) x ≠...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 26th June, 2025

Calculating Length x. tana = 5/10 a = atan(½)° b = 2a b = 2atan(½)° c = 180-2b c = (180-4atan(½))° It implies; x² = 2(10)²-2(10)²cos(180-4atan(½)) x² = 144 x = 12 units.

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 25th June, 2025

Calculating Length x. a = 4+6 a = 10 units. a is the side length of the square. b = 10-3 b = 7 units. c = 10-2-3 c = 5 units. d² = 7²+4² d = √(49+16) d = √(65) units. tane = 4/7...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 25th June, 2025

Calculating Shaded Area. a = 4(4) a = 16 units. a is AB. b = a+4 b = 20 units. b is AC. It implies; 15²+20² = 7²+c² 225+400-49 = c² c = 24 units. c is CE. d = ½(c) d = 12 units. d is CD = DE. d...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 25th June, 2025

Calculating alpha. Let it be a. Let the three equal lengths be 1 units each. b = 180-30-7.5 b = 142.5 ° b is angle AKC. Notice. Angle CAK = Angle KBC = 7.5° (1/sin30) = (c/sin7.5) c = 0.2610523...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 25th June, 2025

Calculating Shaded Area. a² = 1²-(4k)² a = √(1-16k²) units. 1 ~ √(1-16k²) 4k ~ b Cross Multiply. b = 4k√(1-16k²) units. Again. 1 ~ √(1-16k²) √(1-16k²) ~ c Cross Multiply. c = (1-16k²) units....

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 24th June, 2025

a = x° b = (90-x)° R² = 6²+16²-2*6*16cosx R² = 292-192cosx cosx = (292-R²)/192 --- (1). Notice. At (1). (292-R²) is adjacent. 192 is hypotenuse. Let c be opposite. c² = 1...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 24th June, 2025

Let the radius of the ascribed circle be 2 units. Therefore, radius of the bigger inscribed circle is 1 unit. a = (1+y) units b = (2-y) units. c = (1-y) units. Calculating y, radius of the big...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 24th June, 2025

Notice. The ascribed quadrilateral is a square. Let it's side length be x. a²+x² = 3² a = √(9-x²) units. 2 ~ 3 b ~ x Cross Multiply. b = ⅓(2x) units. It implies; Calculating x. x²-½(x*√(...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 23rd June, 2025

Let OA be 1 unit. Area Triangle AOB is; ½*1*1 = ½ square units. Calculating Area Triangle ODG. a² =2(1)²-2(1)²cos30 a = √(2-√(3)) units. a = 0.51763809021 units. a is AC, the side length of the...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 23rd June, 2025

Let a = 1 unit. It implies; 1 ~ b b ~ e Cross Multiply. e = b² f = (1-b²) units. cos60 = g/(1-b) g = ½(1-b) units. h = 2g+1 h = (2-b) units. It implies; Calculating b....

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 23rd June, 2025

Calculating length RT. a = ½(10) a = 5 units. a is half the diagonal of the rectangle. b = 8+a b = 13 units. It implies; (RT)²+5² = 13² RT = √(169-25) RT = √(144) RT = 12 units.

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 23rd June, 2025

Calculating x, length BE. a = 90-75 a = 15° a is angle CBE. sin15 = b/x b = (xsin15) units. b is CE. c = 5+b c = (5+(xsin15)) units. c is CD. cos15 = d/x d = (xcos15) units. d is BC. Notice. c...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 22nd June, 2025

Let the length of the rectangle be a. Let the width of the rectangle be (6+b) units. ½(2a-4)(6+b)-70 = ½(6a)+½(a-4)b 12a+2ab-24-4b-140 = 6a+ab-4b 6a+ab = 164 Therefore; a(6+b) = 164 Notice....

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 22nd June, 2025

Let the side length of the square be x. a = (x-4) units. Calculating x. ½(x²) = ½*x(x-4)-10+30 x² = x(x-4)+40 x² = x²-4x+40 4x = 40 x = 10 units. Again, x is the side length of the square. A...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 22nd June, 2025

Calculating R, radius of the circle. 12a = 3*4 a = 1 unit. b = ½(3+4) b = 3.5 units. c = b-3 c = 0.5 units. d = 180-60 d = 120° e² = R²-3.5² e =√(R²-12.25) units. f² = 1²+0.5...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 21st June, 2025

Calculating R, radius of the quarter circle. a = 3+4 a = 7 units. b² = 2(4)² b = 4√(2) units. c = R-b c = (R-4√(2)) units. d = 180-45 d = 135° R is; R² = 7²+(R-4√(2))²-2*7(R-4√(2))cos135 R² =...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 21st June, 2025

Let BF be a. b² = 18²+a² b = √(324+a²) units. b is AB. c = (a+14) units. It implies; calculating a. (a+14) ~ √(324+a²) √(324+a²) ~ 18 Cross Multiply. 18(a+14) = 324+a² 18a+252 = 324+a² a²-18a+...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 21st June, 2025

Let the side length of the inscribed regular triangle be a. 2b² = a² b = √(a²/2) b = ½√(2)a units. c = 2b c = √(2)a units. c is the side length of the ascribed square. d² = b²+c² d² = (√(2)a)²+(½...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 21st June, 2025

Let AB be 1 unit. Let BC be a. Therefore; CD = (1-a) units. It implies; tan60 = b/(0.5a) 2b = √(3)a b = ½√(3)a units. b is the height of the bigger inscribed equilateral triangle....

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 20th June, 2025

Calculating Blue Area. a = 8+2 a = 10 units. a is the side length of the ascribed square and the radius of the bigger inscribed quarter circle. b = 8 units. b is the radius of the big insc...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 20th June, 2025

Let angle AOB be a. Let b = AD = OB = OD. b is the radius of the quarter circle. Calculating b. 2² = 2b²-2b²cosa 2b²cosa = 2b²-4 b²cosa = b²-2 cosa = (b²-2)/b² --- (1). 4² = b²+(2b)²-4b²cosa 16...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 20th June, 2025

Let r = 1 unit. a = (R+1) units. b = (R-1) units. c²+b² = a² c²+(R-1)² = (R+1)² c² = R²+2R+1-(R²-2R+1) c = √(4R) c = 2√(R) units. d = R+2-R d = 2 units. e = R+R e = 2R units. Calculating R....

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 19th June, 2025

Notice. The ascribed quadrilateral is regular (square). Let a be it's side length. ½*ab = 3 ab = 6 b = (6/a) units. b is the base of the red area. ½*ac = 4 ac = 8 c = (8/a) units....

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 19th June, 2025

tan60 = a/(0.5*8) a = 4tan60 a = 4√(3) cm. a is the diameter of the circle. b = ½(a) b = 2√(3) cm. b is the radius of the circle. c = ¼(8) c = 2 cm. c is the radius of the two equal half circles....

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 19th June, 2025

a = 4+4 a = 8 units. a is the radius of the quarter circle. cosb = ⅛(0.5*4) b = acos(¼)° cosb = c/8 c = 8cos(acos(¼)) c = ¼(8) c = 2 units. c is the width of the inscribed rectangle. sinb = d/8...

Mathematics Question and Solution

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Mathematics Question and Solution

By OnlineEdumath | 18th June, 2025

Let AD = BC = 1 unit. a = 180-100-30 a = 50° a is angle BAC. (1/sin50) = (b/sin30) b = 0.65270364467 units. b is AC. Therefore, the required angle theta is, let it be c. (0.65270364...

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