Diagonal intersect

isosceles trapezoid ABCD with length bases | AB | = 6 cm, CD | = 4 cm is divided into 4 triangles by the diagonals intersecting at point S. How much of the area of the trapezoid are ABS and CDS triangles?

Result

r1 =  0.36
r2 =  0.16

Solution:

a=6 cm c=4 cm  h=h1+h2 h1:h2=a:c  h1=h aa+c  S=a+c2 h  S1=a h12 S2=c h22  r1=S1/S=a h12/(a+c) h2 r1=a h1(a+c) h  r1=a h aa+c(a+c) h r1=a aa+c(a+c)  r1=r1=a2(a+c)2=62(6+4)2=925=0.36a=6 \ \text{cm} \ \\ c=4 \ \text{cm} \ \\ \ \\ h=h_{ 1 }+h_{ 2 } \ \\ h_{ 1 }:h_{ 2 }=a:c \ \\ \ \\ h_{ 1 }=h \cdot \ \dfrac{ a }{ a+c } \ \\ \ \\ S=\dfrac{ a+c }{ 2 } \cdot \ h \ \\ \ \\ S_{ 1 }=\dfrac{ a \cdot \ h_{ 1 } }{ 2 } \ \\ S_{ 2 }=\dfrac{ c \cdot \ h_{ 2 } }{ 2 } \ \\ \ \\ r_{ 1 }=S_{ 1 }/S=\dfrac{ a \cdot \ h_{ 1 } }{ 2 } / \dfrac{ (a+c) \cdot \ h }{ 2 } \ \\ r_{ 1 }=\dfrac{ a \cdot \ h_{ 1 } }{ (a+c) \cdot \ h } \ \\ \ \\ r_{ 1 }=\dfrac{ a \cdot \ h \cdot \ \dfrac{ a }{ a+c } }{ (a+c) \cdot \ h } \ \\ r_{ 1 }=\dfrac{ a \cdot \ \dfrac{ a }{ a+c } }{ (a+c) } \ \\ \ \\ r_{1}=r_{ 1 }=\dfrac{ a^2 }{ (a+c)^2 }=\dfrac{ 6^2 }{ (6+4)^2 }=\dfrac{ 9 }{ 25 }=0.36
r2=S2/S=c h22/(a+c) h2 r2=c h2(a+c) h  r2=c h ca+c(a+c) h r2=c ca+c(a+c)  r2=r2=c2(a+c)2=42(6+4)2=425=0.16r_{ 2 }=S_{ 2 }/S=\dfrac{ c \cdot \ h_{ 2 } }{ 2 } / \dfrac{ (a+c) \cdot \ h }{ 2 } \ \\ r_{ 2 }=\dfrac{ c \cdot \ h_{ 2 } }{ (a+c) \cdot \ h } \ \\ \ \\ r_{ 2 }=\dfrac{ c \cdot \ h \cdot \ \dfrac{ c }{ a+c } }{ (a+c) \cdot \ h } \ \\ r_{ 2 }=\dfrac{ c \cdot \ \dfrac{ c }{ a+c } }{ (a+c) } \ \\ \ \\ r_{2}=r_{ 2 }=\dfrac{ c^2 }{ (a+c)^2 }=\dfrac{ 4^2 }{ (6+4)^2 }=\dfrac{ 4 }{ 25 }=0.16



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!
avatar




Tips to related online calculators
Check out our ratio calculator.

Next similar math problems:

  1. Trapezoid - diagonal
    licho Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm2. What is the area of the trapezoid?
  2. Line
    skew_lines It is true that the lines that do not intersect are parallel?
  3. Orchard
    lichobeznik_1 Route passes trapezoidal orchard perpendicular to the parallel sides. It is 80 cm wide. The lengths of the bases are in the ratio 5:3 and the length of the longer base to the length of the path is in the ratio 5:6. How many square meters occupies the rou
  4. Trapezoid - central median
    lichobeznik-stredni_pricka The central median divides the trapezoid into two smaller trapezoids. Determines the ratio of their contents.
  5. Parametric equation
    line Find the parametric equation of a line with y-intercept (0,-4) and a slope of -2.
  6. Expression with powers
    eq222_9 If x-1/x=5, find the value of x4+1/x4
  7. 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
  8. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  9. 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?
  10. Coefficient
    gp Determine the coefficient of this sequence: 7.2; 2.4; 0.8
  11. Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)
  12. Sequence
    a_sequence Write the first 7 members of an arithmetic sequence: a1=-3, d=6.
  13. Sequence
    mandlebrot Find the common ratio of the sequence -3, -1.5, -0.75, -0.375, -0.1875. Ratio write as decimal number rounded to tenth.
  14. Three workshops
    workers_24 There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
  15. Slope
    slope What is the slope of the line defined by the equation -2x +3y = -1 ?
  16. AP - simple
    sigma_1 Determine the first nine elements of sequence if a10 = -1 and d = 4
  17. Blocks
    cubes3_1 There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?