Rhombus 2

Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.

Result

S =  2400 mm2

Solution:

a=x+y 602=482+y2 y=602−482=36 mm  a2=x2+482 (x+y)2=x2+482 x2+2xy+y2=x2+482 2xy+y2=482 2⋅36⋅x=482−362 x=14 mm  a=x+y=14+36=50 mm  S=av=50⋅48=2400 mm2 a = x+y \ \\ 60^2 = 48^2 + y^2 \ \\ y= \sqrt{ 60^2 - 48^2} = 36 \ mm \ \\ \ \\ a^2 = x^2+48^2 \ \\ (x+y)^2 = x^2+48^2 \ \\ x^2+2xy +y^2 = x^2+48^2 \ \\ 2xy+y^2 = 48^2 \ \\ 2\cdot 36 \cdot x = 48^2 - 36^2 \ \\ x = 14 \ mm \ \\ \ \\ a = x+y = 14 + 36 = 50 \ mm \ \\ \ \\ S = a v = 50 \cdot 48 = 2400 \ \text{mm}^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.

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

Next similar math problems:

  1. Acreage
    pozemek Plot has a diamond shape, its side is 25.6 m long and the distance of the opposite sides is 22.2 meters. Calculate its acreage.
  2. Diagonals in diamons/rhombus
    diamonds Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal.
  3. Park
    diamond_3 In the park is marked diamond shaped line connecting locations A, D, S, C, B, A. Calculate its length if |AB| = 108 m, |AC| = 172.8 m.
  4. Hypotenuse
    RightTriangleMidpoint_1 Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its content area is 16 square centimeters.
  5. Right triangle
    triangles_1 Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides.
  6. Equilateral triangle
    rs_triangle_1 The equilateral triangle has a 23 cm long side. Calculate its content area.
  7. Rectangular triangle PQR
    solving-right-triangles In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal
  8. Four ropes
    vysilac TV transmitter is anchored at a height of 44 meters by four ropes. Each rope is attached at a distance of 55 meters from the heel of the TV transmitter. Calculate how many meters of rope were used in the construction of the transmitter. At each attachment.
  9. Stairway
    schody Stairway has 20 steps. Each step has a length of 22 cm and a height of 15 cm. Calculate the length of the handrail of staircases if on the top and bottom exceeds 10 cm.
  10. Broken tree
    stromy_4 The tree is broken at 4 meters above the ground and the top of the tree touches the ground at a distance of 5 from the trunk. Calculate the original height of the tree.
  11. 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?
  12. Ladder
    rebrik_2 The ladder has a length 3.5 meters. He is leaning against the wall so that his bottom end is 2 meters away from the wall. Determine the height of the ladder.
  13. 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?
  14. 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)?
  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. 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?