# Heron's formula - high school - 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:$S= \sqrt {s(s-a)(s-b)(s-c)}$

, where $s=\dfrac {a+b+c}{2}$

is the semiperimeter (half perimeter) of the triangle .#### Number of problems found: 25

- Compute 4

Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long. - Quadrilateral oblique prism

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°. - Circular railway

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? - 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. - 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 - 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. - 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. - Sails

We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail? - Box

Cardboard box shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm and one diagonal 8 cm long and height of the box is 12 cm. The box will open at the top. How many cm^{2}of cardboard we need to cover overlap and joints that are 5% of are - Four sides of trapezoid

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

Calculate triangle sides where its area is S = 84 cm^{2}and a = x, b = x + 1, xc = x + 2 - Area and two angles

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°. - Sides ratio

Calculate the circumference of a triangle with area 84 cm^{2}if a:b:c = 10:17:21 - Park

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 ABC

Calculate the sides of triangle ABC with area 1404 cm^{2}and if a: b: c = 12:7:18 - 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. - The farmer

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 - Cardboard box

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

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.

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