Heron's formula - 9th grade (14y) - 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: 20

  • 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
  • Sss triangle
    8_11_12 Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
  • One trapezium
    trapezium_5 One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area.
  • Sides ratio
    triangle3_1 Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
  • 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.
  • 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
  • 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
  • Diamond
    diamond_1 Rhombus has side 17 cm and and one of diagonal 22 cm long. 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.
  • Prism
    prism_rhombus_1 Calculate the volume of the rhombic prism. Base of prism is rhombus whose one diagonal is 47 cm and the edge of the base is 28 cm. The edge length of the base of the prism and height is 3:5.
  • Circles 2
    zlozite_kruznice Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
  • Sails
    ship_nina We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
  • 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.
  • 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.
  • Trapezoid
    trapezoid_1 Calculate area of trapezoid ABCD with sides |AD|= 68 cm, |DC|=35 cm, |CB|=12 cm, |AB|=35 cm..
  • Triangle SSS
    triangle_ABC Calculate perimeter and area of ​​a triangle ABC, if a=53, b=46 and c=40.

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