Diagonals at right angle

In the trapezoid ABCD this is given:
AB=12cm
CD=4cm
And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?

Correct result:

S =  64 cm2

Solution:

a=12 cm c=4 cm  a:c=h1:h2  h=h1+h2  h1=a/2=12/2=6 cm h2=c/2=4/2=2 cm  h=h1+h2=6+2=8 cm  S=a+c2⋅ h=12+42⋅ 8=64 cm2a=12 \ \text{cm} \ \\ c=4 \ \text{cm} \ \\ \ \\ a:c=h_{1}:h_{2} \ \\ \ \\ h=h_{1}+h_{2} \ \\ \ \\ h_{1}=a/2=12/2=6 \ \text{cm} \ \\ h_{2}=c/2=4/2=2 \ \text{cm} \ \\ \ \\ h=h_{1}+h_{2}=6+2=8 \ \text{cm} \ \\ \ \\ S=\dfrac{ a+c }{ 2 } \cdot \ h=\dfrac{ 12+4 }{ 2 } \cdot \ 8=64 \ \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!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
See also our 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

Next similar math problems:

  • The trapezium
    rt_iso_triangle The trapezium is formed by cutting the top of the right-angled isosceles triangle. The base of the trapezium is 10 cm and the top is 5 cm. Find the area of trapezium.
  • Trapezoid - RR
    right_trapezium Find the area of the right angled trapezoid ABCD with the right angle at the A vertex; a = 3 dm b = 5 dm c = 6 dm d = 4 dm
  • Semicircle
    tales-de-mileto In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
  • Isosceles trapezoid
    licho_1 Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.
  • Right triangle
    triangles_1 Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides.
  • Height
    thales_law Is right that in any right triangle height is less or equal half of the hypotenuse?
  • Mysterious area
    lichobeznik The trapezoid ABCD is given. Calculate its area if the area of the DBC triangle is 27 cm2.
  • Cross section
    trapezium_right The cross-section ABCD of a swimming pool is a trapezium. Its width AB=14 meters, depth at the shallow end is 1.5 meters, and at the deep end is 8 meters. Find the area of the cross-section.
  • 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?
  • 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?
  • Parcel
    2186094 parcel has a rectangular shape of a trapezoid with bases 12 m and 10 m and a height 8 m. On parcel was built object with a footprint an isosceles triangle shape with side 4 m and height three-quarters of a meter. What is the area of unbuild parcel?
  • Trapezium
    trapezium_1 The area of trapezium is 35cm2 find its altitude if the bases are 6cm and 8cm.
  • Trapezium
    trapezium_1 The area of trapezium is 35 cm2. Find its altitude if the bases are 6cm and 8 cm.
  • 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?
  • Similarity coefficient
    trig12 The triangles ABC and A "B" C "are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A "B" C ".
  • Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  • An equilateral
    goat__wolf_and_cabbage_1 An equilateral triangle with a side 10 m represents a wooden platform standing in a lawn. A goat is tied to a corner with a 15 m rope. What is the maximum amount of grazing area available to the goat?