Divide an isosceles triangle

How to divide an isosceles triangle into two parts with equal contents perpendicular to the axis of symmetry (into a trapezoid and a triangle)?

Correct answer:

x =  1.4142

Step-by-step explanation:

h2:a2=h:a h2=h a2/a  S1=h2 a22=a22 h2 a  S2=a+a22 h(1a2/a)  S1=S2  a22 h2 a=a+a22 h(1a2/a)  a22=(a+2) (aa2)=0 a22=a2a22 2 a22=a2  2a2=a  h2=h a2/a=a22 a2=1/2  x=h:h2  x=2=1.4142



Did you find an error or inaccuracy? Feel free to write us. Thank you!



avatar




Tips to related online calculators
See also our right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions:

  • Hexagon = 8 parts
    stef.6.11.99 Divide the regular hexagon into eight equal parts.
  • MO Z8–I–6 2018
    lich In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.
  • Diagonal in rectangle
    q In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts.
  • Isosceles trapezoid
    rr_lichobeznik Find the area of an isosceles trapezoid with bases of 8cm and 72mm. The height of the trapezoid is equal to three-quarters of the longer base.
  • Inner angles
    rr_triangle3 The magnitude of the internal angle at the main vertex C of the isosceles triangle ABC is 72°. The line p, parallel to the base of this triangle, divides the triangle into a trapezoid and a smaller triangle. How big are the inner angles of the trapezoid?
  • MO - triangles
    metal On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB seg
  • Isosceles trapezoid
    rr_lichobeznik Calculate the circumference and the contents of the isosceles trapezoid if you know the size of the bases is 8 and 12 cm and the size of the arms is 5 cm.
  • Isosceles trapezoid
    lichobeznik In an isosceles trapezoid KLMN intersection of the diagonals is marked by the letter S. Calculate the area of trapezoid if /KS/: /SM/ = 2:1 and a triangle KSN is 14 cm2.
  • Embankment
    sss Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long.
  • Construction of trapezoid
    lichobeznik Construct a trapezoid if b = 4cm, c = 7cm, d = 4,5cm, v = 3 cm (Procedure, discussion, sketch, analysis, construction)
  • Construct 1
    thales_right Construct a triangle ABC, a = 7 cm, b = 9 cm with right angle at C, construct the axis of all three sides. Measure the length of side c (and write).
  • Sides od triangle
    podobnost Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm.
  • Divide in ratio
    lines Line segment AB 12 cm long divide in a ratio of 5: 3. How long are the individual parts?
  • Draw a trapezoid
    konstrukter Draw a trapezoid if given a = 7 cm, b = 4 cm, c = 3.5 cm, diagonal AC = 5cm. Solve as a construction task.
  • Area of iso-trap
    diagons-of-an-isosceles-trapezoid Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other.
  • Road embankment
    nasyp_cesta Road embankment has a cross-section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters?
  • Similarity of squares
    squares2 The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ?