Heron's formula - practice problems - page 3 of 4
The Heron's formula is used to calculate the area 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=s(s−a)(s−b)(s−c), where s=2a+b+c is the semiperimeter (half perimeter) of the triangle .
Direction: Solve each problem carefully and show your solution in each item.
Number of problems found: 63
- Parallelogram 5027
Calculate the area of the parallelogram if the side sizes are a = 80, b = 60, and the size of the diagonal angle is 60°. - Park
The newly built park will be permanently placed with rotating sprayer irrigation lawns. Find the largest radius of the circle that can irrigate by sprayer P, not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m. - Calculate 82696
In the triangle ABC, b=5 cm, c=6 cm, /BAC/ = 80° are given. Calculate the sizes of the other sides and angles, and further determine the sizes of the tangent tc and the area of the triangle. - Irregular hexagon
There is an irregular hexagon whose sides are the same length. The opposite sides are parallel; their distance is 237, 195, and193. What is its area? - Gardens
The area of the square garden is 3/4 of the area of the triangular garden with sides of 80 m, 50 m, and 50 m. How many meters of fence do we need to fence a square garden? - A Cartesian framework
1. In a Cartesian framework, the functions f and g we know that: The function (f) is defined by f (x) = 2x², the function (g) is defined by g (x) = x + 3, the point (O) is the origin of the reference, and point (C) is the point of intersection of the grap - Triangle
Plane coordinates of vertices: K[19, -4] L[9, 13] M[-20, 8] give Triangle KLM. Calculate its area and its interior angles. - Circumference 64104
The ABC triangle has a circumference of 11 cm. Triangle A'B'C ', similar to triangle ABC, has side lengths of 6 cm, 120 mm, and 1.5 dm larger than triangle ABC. Calculate the area of the triangle A'B'C '. - 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 interior angles α = 15°28' and β = 45°. - Directional 2595
Calculate the interior angles of triangle ABC using vectors. Coordinates A [2; 4] B [4; 6] C [0; -4]. Calculate directional vectors of sides, parametric and general equations of sides, parametric and general equations of lines, calculate area, calculate h - The triangle 5
The triangle below has vertices A(-1,-2), B(2,2), and C(-1,4). What is the area of △ABCin square coordinate units? - Sides ratio
Calculate the circumference of a triangle with area 84 cm² if a:b:c = 10:17:21 - Calculate 82144
Calculate the height of side b (v_b) of triangle ABC with vertices A[4;1;3] B[2;3;3] and C[1;1;3]. - Vertex points
Suppose 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
The trapezoid is given by the length of four sides: 40.5 42.5 52.8 35.0. Calculate its area. - Cardboard box
We want to make a cardboard box-shaped quadrangular prism with a rhombic base. The rhombus has a side of 5 cm and 8 cm, one diagonal long. The height of the box is 12 cm. The box will be open at the top. How many square centimeters do we need if we calcul - Box
The cardboard is a box-shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm, one diagonal 8 cm long, and the box's height is 12 cm. The package will open at the top. How many cm² of cardboard do we need to cover overlap and joints that a - Prism-shaped 6137
The prism-shaped vessel with a rhomboid base has one base diagonal of 10 cm and the edge of the base 14 cm. The edge of the base and the prism height are in a ratio of 2:5. How many liters of water is in the container when it is filled to four-fifths of t - 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°? - Calculate 23411
The prism with a diamond base has one base diagonal of 20 cm and a base edge of 26 cm. The edge of the base is 2:3 to the height of the prism. Calculate the volume of the prism.
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