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=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}=\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=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}=\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. Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  2. Coordinates of a centroind
    triangle_234 Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians).
  3. Two people
    crossing Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apa
  4. Coordinates of square vertices
    ctverec_2 The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square.
  5. Find the 10
    lines Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?
  6. Find the 5
    distance-between-point-line Find the equation with center at (1,20) which touches the line 8x+5y-19=0
  7. Right triangle from axes
    axes2 A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
  8. Right angled triangle 2
    vertex_triangle_right LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n
  9. Cuboids
    3dvectors Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
  10. Parametric form
    vzdalenost Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. ..
  11. Three points 2
    vectors_sum0 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
  12. Vector equation
    collinear2 Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent
  13. Set of coordinates
    axes2 Consider the following ordered pairs that represent a relation. {(–4, –7), (0, 6), (5, –3), (5, 2)} What can be concluded of the domain and range for this relation?
  14. Points collinear
    collinear Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
  15. Line
    negative_slope Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
  16. Angle between vectors
    arccos Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
  17. Slope form
    lines_2 Find the equation of a line given the point X(8, 1) and slope -2.8. Arrange your answer in the form y = ax + b, where a, b are the constants.