Area of iso-trap

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.

Result

A =  529 cm2

Solution:

c=16 cm a=30 cm  a2=x2+x2 x=a/2=30/2≐15 2 cm≐21.2132 cm  c2=y2+y2 y=c/2=16/2≐8 2 cm≐11.3137 cm  d=x+y=21.2132+11.3137≐23 2 cm≐32.5269 cm  h1=x2−(a/2)2=21.21322−(30/2)2=15 cm h2=y2−(c/2)2=11.31372−(16/2)2=8 cm  h=h1+h2=15+8=23 cm  A1=a+c2⋅ h=30+162⋅ 23=529 cm2  A=d⋅ d2=32.5269⋅ 32.52692=529 cm2c=16 \ \text{cm} \ \\ a=30 \ \text{cm} \ \\ \ \\ a^2=x^2 + x^2 \ \\ x=a / \sqrt{ 2 }=30 / \sqrt{ 2 } \doteq 15 \ \sqrt{ 2 } \ \text{cm} \doteq 21.2132 \ \text{cm} \ \\ \ \\ c^2=y^2 + y^2 \ \\ y=c / \sqrt{ 2 }=16 / \sqrt{ 2 } \doteq 8 \ \sqrt{ 2 } \ \text{cm} \doteq 11.3137 \ \text{cm} \ \\ \ \\ d=x+y=21.2132+11.3137 \doteq 23 \ \sqrt{ 2 } \ \text{cm} \doteq 32.5269 \ \text{cm} \ \\ \ \\ h_{ 1 }=\sqrt{ x^2-(a/2)^2 }=\sqrt{ 21.2132^2-(30/2)^2 }=15 \ \text{cm} \ \\ h_{ 2 }=\sqrt{ y^2-(c/2)^2 }=\sqrt{ 11.3137^2-(16/2)^2 }=8 \ \text{cm} \ \\ \ \\ h=h_{ 1 }+h_{ 2 }=15+8=23 \ \text{cm} \ \\ \ \\ A_{ 1 }=\dfrac{ a+c }{ 2 } \cdot \ h=\dfrac{ 30+16 }{ 2 } \cdot \ 23=529 \ \text{cm}^2 \ \\ \ \\ A=\dfrac{ d \cdot \ d }{ 2 }=\dfrac{ 32.5269 \cdot \ 32.5269 }{ 2 }=529 \ \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
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Diagonal
    trapezium_right_1 he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
  2. Calculate
    equilateral_triangle2 Calculate the length of a side of the equilateral triangle with an area of 50cm2.
  3. A kite
    kite2 ABCD is a kite. Angle OBC = 20° and angle OCD = 35°. O is the intersection of diagonals. Find angle ABC, angle ADC and angle BAD.
  4. Rectangular trapezoid
    rt_trapezium In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v.
  5. Ditch
    lichob_2_1 Ditch profile is an isosceles trapezoid with bases of length 80m and 60m. The slope of the side wall of the ditch is 80°. Calculate the ditch depth.
  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. 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?
  8. Find the 9
    obtuse_triangle_1 Find the missing angle in the triangle and then name triangle. Angles are: 95, 2x+15, x+3
  9. Satin
    diagonal_rectangle_3 Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?
  10. 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).
  11. 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?
  12. Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  13. Fifth of the number
    numbs_5 The fifth of the number is by 24 less than that number. What is the number?
  14. 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?
  15. 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?
  16. 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)?
  17. A mast
    stoziar_1 A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken?