The sides 2

The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.

Result

h =  14
o =  70

Solution:

a:b:c:d=2:5:8:5 a=8x b=d=5x c=2x ac  S=245  h=d2((ac)/2)2 h=x 52((82)/2)2  h=x 52((82)/2)2 h=x 16 h=4x  S=a+c2h S=8x+2x2h S=8x+2x2 4x S=5x 4x x=S/20=245/20=72=3.5  h=4 x=4 3.5=14a:b:c:d=2:5:8:5 \ \\ a=8x \ \\ b=d=5x \ \\ c=2x \ \\ a || c \ \\ \ \\ S=245 \ \\ \ \\ h=\sqrt{ d^2 - ((a-c)/2)^2 } \ \\ h=x \cdot \ \sqrt{ 5^2 - ((8-2)/2)^2 } \ \\ \ \\ h=x \cdot \ \sqrt{ 5^2 - ((8-2)/2)^2 } \ \\ h=x \cdot \ \sqrt{ 16 } \ \\ h=4x \ \\ \ \\ S=\dfrac{ a+c }{ 2 } h \ \\ S=\dfrac{ 8x+2x }{ 2 } h \ \\ S=\dfrac{ 8x+2x }{ 2 } \cdot \ 4x \ \\ S=5x \cdot \ 4x \ \\ x=\sqrt{ S/20 }=\sqrt{ 245/20 }=\dfrac{ 7 }{ 2 }=3.5 \ \\ \ \\ h=4 \cdot \ x=4 \cdot \ 3.5=14
a=8 x=8 3.5=28 b=5 x=5 3.5=352=17.5 d=5 x=5 3.5=352=17.5 c=2 x=2 3.5=7  S1=a+c2 h=28+72 14=245 S1=S  o=a+b+c+d=28+17.5+7+17.5=70a=8 \cdot \ x=8 \cdot \ 3.5=28 \ \\ b=5 \cdot \ x=5 \cdot \ 3.5=\dfrac{ 35 }{ 2 }=17.5 \ \\ d=5 \cdot \ x=5 \cdot \ 3.5=\dfrac{ 35 }{ 2 }=17.5 \ \\ c=2 \cdot \ x=2 \cdot \ 3.5=7 \ \\ \ \\ S_{1}=\dfrac{ a+c }{ 2 } \cdot \ h=\dfrac{ 28+7 }{ 2 } \cdot \ 14=245 \ \\ S_{1}=S \ \\ \ \\ o=a+b+c+d=28+17.5+7+17.5=70



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 1 comment:
#
Math student
I don't understand.

avatar









Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

Next similar math problems:

  1. Sum of squares
    pytagorean The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.
  2. Land - isosceles trapezoid
    lichobeznik-stredni_pricka_1 Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
  3. Roof tiles
    Lichobeznik_strecha The roof has a trapezoidal shape with bases of 15 m and 10 m, height of roof is 4 meters. How many tiles will need if on 1 m2 should be used 8 tiles?
  4. Length IT
    lich2 Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c and the height h are given: a = 8 cm c = 2 cm h = 4 cm
  5. Isosceles trapezoid
    lichobeznik_mo_z8_5 What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
  6. The ditch
    prikop Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch?
  7. Estate
    mapa Estate shaped rectangular trapezoid has bases long 34 m , 63 m and perpendicular arm 37 m. Calculate how long is its fence.
  8. Isosceles triangle
    triangles_8 Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.
  9. Land
    12-13-5-triangle Rectangular triangular land has area 30 square meters and 12 meters long leg. How many meters of the fence do you need for fencing this land?
  10. Equilateral triangle
    rs_triangle_1 The equilateral triangle has a 23 cm long side. Calculate its content area.
  11. Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  12. The double ladder
    dvojity_rebrik The double ladder has 3 meters long shoulders. What is the height of the upper of the ladder reach if the lower ends are 1.8 meters apart?
  13. Ladder
    rebrik33_4 Adam placed the ladder of the house, the upper end reaching to the window at the height of 3.6m, and the lower end standing on level ground and was distant from a wall of 1.5m. What is the length of the ladder?
  14. Median in right triangle
    rt_triangle In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
  15. The ladder
    rebrik33_1 The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?
  16. 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?
  17. Center traverse
    trianles It is true that the middle traverse bisects the triangle?