Four sides of trapezoid

Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.

Result

S =  1414.594

Solution:

a=40.5 b=42.5 c=52.8 d=35.0  x=c−a=52.8−40.5=12310=12.3 s=(b+d+x)/2=(42.5+35+12.3)/2=44910=44.9 S1=s⋅ (s−b)⋅ (s−d)⋅ (s−x)=44.9⋅ (44.9−42.5)⋅ (44.9−35)⋅ (44.9−12.3)≐186.4898 h=2⋅ S1/x=2⋅ 186.4898/12.3≐30.3236 S2=a⋅ h=40.5⋅ 30.3236≐1228.1039 S=S1+S2=186.4898+1228.1039≐1414.5937=1414.594a = 40.5 \ \\ b = 42.5 \ \\ c = 52.8 \ \\ d = 35.0 \ \\ \ \\ x = c-a = 52.8-40.5 = \dfrac{ 123 }{ 10 } = 12.3 \ \\ s = (b+d+x)/2 = (42.5+35+12.3)/2 = \dfrac{ 449 }{ 10 } = 44.9 \ \\ S_{ 1 } = \sqrt{ s \cdot \ (s-b) \cdot \ (s-d) \cdot \ (s-x) } = \sqrt{ 44.9 \cdot \ (44.9-42.5) \cdot \ (44.9-35) \cdot \ (44.9-12.3) } \doteq 186.4898 \ \\ h = 2 \cdot \ S_{ 1 }/x = 2 \cdot \ 186.4898/12.3 \doteq 30.3236 \ \\ S_{ 2 } = a \cdot \ h = 40.5 \cdot \ 30.3236 \doteq 1228.1039 \ \\ S = S_{ 1 }+S_{ 2 } = 186.4898+1228.1039 \doteq 1414.5937 = 1414.594

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
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
See also our trigonometric triangle calculator.

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

Next similar math problems:

  1. In a 2
    angles_7 In a thirteen sided polygon, the sum of five angles is 1274°, four of the eight angles remaining are equal and the other four are 18° less than each of the equal angles. Find the angles. .
  2. Trapezoid
    trapezoid_1 Calculate area of trapezoid ABCD with sides |AD|= 68 cm, |DC|=35 cm, |CB|=12 cm, |AB|=35 cm..
  3. Trapezium
    lichobeznik_mo_z8_2 The lengths of a parallel sides of a trapezium are (2x+3) and (x+8) and the distance between them is (x+4). if the area of the trapezium is 590 , find the value of x.
  4. Triangle
    triangle_ABC_1 The triangle has known all three sides: a=5.5 m, b=5.3 m, c= 7.8 m. Calculate area of ​this triangle.
  5. Circles 2
    zlozite_kruznice Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
  6. Sides of the triangle
    herons Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2
  7. Sss triangle
    8_11_12 Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
  8. The farmer
    field_2 The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine t
  9. Isosceles trapezoid
    lichobeznik Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid.
  10. Trapezoid - hard example
    trapezium Base of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter.
  11. Area of ditch
    prikop How great content area will have a section of trapezoidal ditch with a width of 1.6 meters above and below 0.57 meters? The depth of the ditch is 2.08 meters.
  12. 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
  13. Roof
    roof Tiles are stacked in rows on the trapezoidal shaped roof. At the ridge is 15 tiles and each subsequent row has one more tile than in the previous row. How many tiled is covered roof if lowermost row has 37 tiles?
  14. AS sequence
    AP In an arithmetic sequence is given the difference d = -3 and a71 = 455. a) Determine the value of a62 b) Determine the sum of 71 members.
  15. Center
    triangle_axis Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
  16. Sails
    ship_nina We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
  17. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?