Heron's formula + triangle - math 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) S= \sqrt {s(s-a)(s-b)(s-c)}
, where
s=a+b+c2s=\dfrac {a+b+c}{2}
is the semiperimeter (half perimeter) of the triangle .

Number of problems found: 31

  • Given 2
    PQR_triangle Given the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find triangle area.
  • Compute 4
    14-12-12 Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long.
  • Annulus from triangle
    annulus2 Calculate the content of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm
  • One trapezium
    trapezium_5 One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area.
  • Quadrilateral oblique prism
    kosyHranol What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35 ´ and the edges a, b form an angle of 50.5°.
  • Is right triangle or not
    triangle_rt1_2 If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
  • Triangular prism
    688_triangle Calculate the surface of a triangular prism 10 cm high, the base of which is a triangle with sides 6 cm 8 cm and 8 cm
  • Circular railway
    described_circle2 The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
  • Sss triangle
    8_11_12 Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
  • Cardboard box
    krabicka We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we ca
  • Sides ratio
    triangle3_1 Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
  • Area and two angles
    trig_1 Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°.
  • Four sides of trapezoid
    lichobeznik2 Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.
  • Park
    park_voda In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
  • 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
  • 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.
  • 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 th
  • Sails
    ship_nina We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
  • Sides of the triangle
    herons Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2
  • Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles.

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