Three faces of a cuboid

The diagonal of three faces of a cuboid are 13,√281 and 20 units. Then the total surface area of the cuboid is.


S =  664


d1=13 d2=281=28116.7631 d3=20  d12=a2+b2 d22=b2+c2 d32=a2+c2  a2=d12b2=d12d22+c2=d12d22+d32a2 2a2=d12d22+d32  a=d12d22+d322=13216.76312+2022=12  ... b=d12+d22d322=132+16.763122022=5  ... c=d12+d22+d322=132+16.76312+2022=16  S=2 (a b+b c+c a)=2 (12 5+5 16+16 12)=664d_{1}=13 \ \\ d_{2}=\sqrt{ 281 }=\sqrt{ 281 } \doteq 16.7631 \ \\ d_{3}=20 \ \\ \ \\ d_{1}^2=a^2+b^2 \ \\ d_{2}^2=b^2+c^2 \ \\ d_{3}^2=a^2+c^2 \ \\ \ \\ a^2=d_{1}^2 - b^2=d_{1}^2-d_{2}^2+c^2=d_{1}^2-d_{2}^2+d_{3}^2-a^2 \ \\ 2a^2=d_{1}^2-d_{2}^2+d_{3}^2 \ \\ \ \\ a=\sqrt{ \dfrac{ d_{1}^2-d_{2}^2+d_{3}^2 }{ 2 } }=\sqrt{ \dfrac{ 13^2-16.7631^2+20^2 }{ 2 } }=12 \ \\ \ \\ ... \ \\ b=\sqrt{ \dfrac{ d_{1}^2+d_{2}^2-d_{3}^2 }{ 2 } }=\sqrt{ \dfrac{ 13^2+16.7631^2-20^2 }{ 2 } }=5 \ \\ \ \\ ... \ \\ c=\sqrt{ \dfrac{ -d_{1}^2+d_{2}^2+d_{3}^2 }{ 2 } }=\sqrt{ \dfrac{ -13^2+16.7631^2+20^2 }{ 2 } }=16 \ \\ \ \\ S=2 \cdot \ (a \cdot \ b+b \cdot \ c+c \cdot \ a)=2 \cdot \ (12 \cdot \ 5+5 \cdot \ 16+16 \cdot \ 12)=664

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!

Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Warehouses
    silo_3 In the three warehouses, a total of 70 tons of grain was stored. In the second warehouse was stored 8.5t less and in the third 3.5t more than in the first. How many tons of grain was stored in each warehouse?
  2. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  3. Three unknowns
    matrix_1 Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0
  4. Football match 4
    futball_ball In a football match with the Italy lost 3 goals with Germans. Totally fell 5 goals in the match. Determine the number of goals of Italy and Germany.
  5. Linsys2
    linear_eq_3 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
  6. Ball game
    lopta_3 Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
  7. Children
    children_3 The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
  8. Men, women and children
    regiojet On the trip went men, women and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus was paid 4,200 crowns?
  9. Null points
    absolute value Calculate the roots of the equation: ?
  10. Stones 3
    stones Simiyu and Nasike each collected a number of stones in an arithmetic lesson. If Simiyu gave Nasike 5 stones, Nasike would have twice as many stones as Simiyu. If initially, Simiyu had five stones less than Nasike how many stones did each have?
  11. Geometric sequence 5
    sequence About members of geometric sequence we know: ? ? Calculate a1 (first member) and q (common ratio or q-coefficient)
  12. Guppies for sale
    guppies Paul had a bowl of guppies for sale. Four customers were milling around the store. 1. Rod told paul - I'll take half the guppies in the bowl, plus had a guppy. 2. Heather said - I'll take half of what you have, plus half a guppy. The third customer, Na
  13. Elimination method
    rovnice_1 Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
  14. Add vector
    vectors_2 Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
  15. AP - basics
    ap Determine first member and differentiate of the the following sequence: a3-a5=24 a4-2a5=61
  16. Intercept with axis
    log_10 F(x)=log(x+4)-2, what is the x intercept
  17. Isosceles trapezoid
    lichobeznik_2 Perimeter of the isosceles trapezoid is 48 cm. One side is two times greater than the second side. Determine the dimensions of the trapezoid.