# 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:
$S=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$
, where
$s=\frac{a+b+c}{2}$
is the semiperimeter (half perimeter) of the triangle .

#### Number of problems found: 33

• Triangle
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
Calculate missing side in a triangle with sides 17 and 34 and area 275.
• Triangle
Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33.
• Triangle SSS
Calculate perimeter and area of ​​a triangle ABC, if a=53, b=46 and c=40.
• Find the area
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
Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2
• Is right triangle or not
If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
• Vertex points
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
Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.
• Triangle
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
Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area.
• Sails
We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
• Sides ratio
Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
• One trapezium
One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area.
• Sss triangle
Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
• Trapezoid - hard example
Base of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter.
• Circles 2
Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
• Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
• Described
Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
• Trapezoid
Calculate the area of trapezoid ABCD with sides |AD|= 68 cm, |DC|=35 cm, |CB|=12 cm, |AB|=35 cm..

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