Heron's formula - high school - math problemsThe 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:
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
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.
We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
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 cm2 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 cm2 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 cm2 if a:b:c = 10:17:21
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 cm2 and if a: b: c = 12:7:18
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
See also our trigonometric triangle calculator. See also more information on Wikipedia.