Isosceles trapezoid

Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.

Correct result:

S =  420 cm2

Solution:

S=(a+c)h/2  a12=b2−h2 a1=b2−h2=132−122=5 cm a=c+2a1 a/c=4/3 (c+2a1)c=4/3 3(c+2a1)=4c 6a1=c c=6a1=6⋅5=30 cm a=c+2a1=30+2⋅5=40 cm  S=(a+c)h/2=(40+30)⋅12/2=420 cm2  S = (a+c)h/2 \ \\ \ \\ a_1^2 = b^2 - h^2 \ \\ a_1 = \sqrt{b^2 - h^2} = \sqrt{ 13^2 - 12^2} = 5 \ cm \ \\ a = c+2a_1 \ \\ a/c = 4/3 \ \\ (c+2a_1)c = 4/3 \ \\ 3(c+2a_1) = 4c \ \\ 6a_1 = c \ \\ c = 6a_1 = 6 \cdot 5 = 30 \ cm \ \\ a = c + 2a_1= 30 + 2\cdot 5 = 40 \ cm \ \\ \ \\ S = (a+c)h/2 = (40 + 30) \cdot 12 /2 = 420 \ \text{cm}^2 \ \\

Try another example


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
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • 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.
  • Isosceles trapezium
    rr_lichobeznik_2 Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
  • ISO trapezoid v2
    lichobeznik bases of Isosceles trapezoid measured 12 cm and 5 cm and its perimeter is 21 cm. What is the are of a trapezoid?
  • 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?
  • Rectangular trapezoid
    color_triangles Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.
  • Estate
    mapa Estate shaped rectangular trapezoid has bases long 34 m , 63 m and perpendicular arm 37 m. Calculate how long is its fence.
  • KLMN trapezoid
    lich_3 The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K?
  • Trapezoid MO-5-Z8
    lichobeznik-stredni_pricka_2 Trapezoid KLMN has bases 12 and 4 cm long. The area of triangle KMN is 9 cm2. What is the area of the trapezoid KLMN?
  • The right triangle
    rt_tr540 The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.
  • Equilateral triangle
    rs_triangle_1 The equilateral triangle has a 23 cm long side. Calculate its content area.
  • Right triangle
    triangles_1 Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides.
  • 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?
  • Windbreak
    vichrica A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?
  • Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  • Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
  • A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  • The ladder
    rebrik The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach?