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

#### Number of problems found: 20

• Compute 4
Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long.
• Annulus from triangle
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
Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
• One trapezium
One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area.
• Sides ratio
Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
• 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
• 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.
• 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
• 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
• Diamond
Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area.
• 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.
• Prism
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
Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
• Sails
We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
• 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.
• 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.
• Trapezoid
Calculate area of trapezoid ABCD with sides |AD|= 68 cm, |DC|=35 cm, |CB|=12 cm, |AB|=35 cm..
• Triangle SSS
Calculate perimeter and area of ​​a triangle ABC, if a=53, b=46 and c=40.

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.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...