Heron's formula - 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 = \frac{a + b + c}{2}

is the semiperimeter (half perimeter) of the triangle .

Number of problems found: 41

Trapezoid and diagonals
Find the area of a trapezoid with bases a = 24 cm, c = 16 cm and diagonals u = 22 cm, v = 26 cm.
Circle inscribed
There is a triangle ABC and a circle inscribed in this triangle with radius 15. The point T is the point of contact of the inscribed circle with the side BC. What is the area of the triangle ABC if | BT | = 25 a | TC | = 26?
Parallelogram ABCD
We have the parallelogram ABCD, where AB is 6.2 cm BC is 5.4 cm AC is 4.8 cm calculate the height on the AB side and the angle DAB
Calculate triangle
In the triangle ABC, calculate the sizes of all heights, angles, perimeters and its area, if given a-40cm, b-57cm, c-59cm
A Cartesian framework
1. In a Cartesian framework, the functions f and g we know that: the function (f) is defined by f (x) = 2x ^ 2, the function (g) is defined by g (x) = x + 3, the point (O) is the origin of the reference, point (C) is the point of intersection of the graph
A rhombus 2
A rhombus have sides of 170 meters and diagonal of 300 meters. What is the area of the rhombus?
Four sides of trapezoid
Calculate the area of the ABCD trapezoid with sides a = 65 cm, b = 29 cm, c = 40 cm, d = 36 cm
Gardens
The area of the square garden is 3/4 of the area of the triangular garden with sides of 80 m, 50 m, 50 m. How many meters of the fence do we need to fence a square garden?
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.
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°.
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
Compute 4
Compute the exact value of the triangle area with sides 14 mi, 12 mi, and 12 mi long.
Circular railway
The railway connects 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?
Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area?
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
Is right triangle or not
If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
Triangular prism
Calculate the surface of a triangular prism 10 cm high, the base of which is a triangle with sides 6 cm 8 cm, and 8 cm
Sides ratio
Calculate the circumference of a triangle with area 84 cm² if a:b:c = 10:17:21
Four sides of trapezoid
Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.