Heron's formula - math word problems

The Heron's formula is used to calculate the contents of a general triangle using the lengths of its sides. Heron's formula states that the area of a triangle whose sides have lengths a, b, and c is:
S=s(sa)(sb)(sc)
, where
s=a+b+c2
is the semiperimeter (half perimeter) of the triangle .

Number of problems found: 33

  • Triangle
    heron1 Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201
  • Heron backlaw
    heron_math Calculate missing side in a triangle with sides 17 and 34 and area 275.
  • Triangle
    trangle_nice Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33.
  • Triangle SSS
    triangle_ABC Calculate perimeter and area of ​​a triangle ABC, if a=53, b=46 and c=40.
  • Find the area
    triangles_57 Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft
  • Sides of the triangle
    herons Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2
  • Is right triangle or not
    triangle_rt1_2 If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
  • Vertex points
    PQR_triangle Given the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area.
  • Four sides of trapezoid
    lichobeznik2 Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.
  • 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.
  • Diamond
    diamond_1 Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area.
  • Sails
    ship_nina We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
  • Sides ratio
    triangle3_1 Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
  • One trapezium
    trapezium_5 One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area.
  • Sss triangle
    8_11_12 Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
  • Trapezoid - hard example
    trapezium Base of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter.
  • Circles 2
    zlozite_kruznice Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
  • Triangle ABC
    triangles_3 Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
  • Described
    desc_circle Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
  • Trapezoid
    trapezoid_1 Calculate the area of trapezoid ABCD with sides |AD|= 68 cm, |DC|=35 cm, |CB|=12 cm, |AB|=35 cm..

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...



See also our trigonometric triangle calculator. See also more information on Wikipedia.