Post a New Question

grade 9 math

posted by .

Trapezoid ABCD, top AD and bottom BC are parallel. AD is the smaller of the two parallel lines. Left AB is 45, bottom BC is 60, right CD is 30, top AD is unknown.

Trapezoid EFGH is similar to ABCD, top EH and bottom FG are parallel. EH is the smaller of the two parallel lines. Top EH is 10, other sides are unknown.

Area of ABCD is 9 times larger than EFGH.

What is the perimeter of EFGH ?

  • grade 9 math -

    The areas of similar figures are proportional to the square of their corresponding sides

    since the areas are in the ratio of 9:1
    the sides are in the ratio of 3:1

    so AD/EH = 3/1
    AD/10 = 3/1
    AD = 30
    Perimeter of ABCD = 165

    Perimeter EFGH/Perimeter ABCD = 1/3
    Perimeter EFGH/165 = 1/3

    perimeter EFGH = 55

  • grade 9 math -

    I am still lost.

    How come the areas of similar figures (trapezoids) are proportional to the squeare of their corresponding perimeters.

  • grade 9 math -

    let me illustrate with an example

    consider the right-angled triange with sides 3, 4, and 5
    (easy to find areas of right-angles triangles)

    a triangle similar is 12, 16, 20 ( I multiplied each side by 4)

    area of smaller = (1/2)(3)(4) = 6
    area of larger = (1/2)(12)(16) = 96

    notice the ratio of their sides = 1:4
    ratio of their areas = 6:96 = 1:16 = 1^2 : 4^2
    which is the square of their sides.

    now look at the perimeters
    per of smaller = 3+4+5 = 12
    per of larger = 12+16+20 = 48

    notice the ratio of perimeters is 12:48 = 1:4
    the same as the ratio of sides

    Perimeter is a linear relationship
    while area is a second degree relationship

    Does that help?

  • grade 9 math -

    Does this work for all trapezoids ?

    Is this true for all similar enclosed figures ?

    Can you help me with my other question posted minutes later than this one ?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    The following figure is a rectangular box in which EFGH and ABCD are rectangles and BF (with a bar on top) is perpendicular to planes EFGH and ABCD.Are BD and GH parallel?
  2. math

    Trapezoid ABCD, top and bottom are parallel. Left is 45, bottom is 60, right is 30, top is unknown. Trapezoid EFGH is similar to ABCD, top and bottom are parallel. Top is 10, other sides are unknown. Area of ABCD is 9 times larger …
  3. Math

    A trapezoid has to have one pair of parallel lines, right?
  4. algebra

    There are two similar triangles. The angles are: from top to bottom left: DE, from bottom left to right: EF, And from Top to bottom right corner: DF. DE: 10.32 cm.EF: 8.88 cm.FD 12.24 cm. The angles are: D,top,45 Degrees. E, bottom …
  5. geometry

    Lines M and T are parallel with a Transversal line P. [Labeling for the angles on line P intersecting M are, top right corner is angle 1, the top left is angle 2, the bottom left is angle 3, and the bottom left is angle 4. This pattern …
  6. GEOMETRY HELPPPPP MEEEE PLEASSEEEEE!!!

    Find the lengths of the diagonals of this trapezoid. trapezoid on a graph with points (-a,0), (-b,c), (b,c), (a,0) negative a and b are on the left side (a is on bottom and b is on top) and positive a and b are on the right side (a …
  7. Math

    Really stuck on this question not sure where im going wrong a trapezium with top and bottom sides paralell. With a diagonal line running from the top left to the bootom right hand corner splitting the trapez into two triangles. the …
  8. Geometry

    I have four questions: 1. The area of trapezoid ABCD is 60. One base is 4 units longer than the other, and the height of the trapezoid is 5. Find the length of the median of the trapezoid. 2. In trapezoid ABCD, line BC is parallel …
  9. Math

    Based on examples she has seen, a child might think that a trapezoid is" a shape with 4 sides, top and bottom are parallel, bottom longer than the top, no sides the same size, large, no right angles, cut off at the top." Which of these …
  10. Geometry

    Find the value of x. There is two lines, they are not parallel. In between (connected) those two lines is a shape. A trapezoid by the looks of it. It is wide at the bottom and thin at the top. There are equations outside of the shape, …

More Similar Questions

Post a New Question