# Heron's formula - practice problems - last page

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: 59

- 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 - Sides ratio

Calculate the circumference of a triangle with area 84 cm² if a:b:c = 10:17:21 - 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? - 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 - 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 - 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 - 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. - Prism

Calculate the volume of the rhombic prism. The prism base is a 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. - Sails

We know heights 220, 165, and 132 of sail. It has a triangular shape. What is the surface of the sail? - Triangular prism

Calculate the surface of a triangular prism 10 cm high, the base of which is a triangle with sides of 6 cm, 8 cm, and 8 cm

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