# 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: 68

- Circumscribed 81759

In triangle ABC, we know a = 4 cm, b = 6 cm, γ = 60°. Calculate the area and radius of the inscribed and circumscribed circle. - Determine 79364

Given a general triangle ABC. Its perimeter is 30 cm, with side a=2 cm longer than side b and 5 cm shorter than side c. Determine the area of the triangle. - Parallelogram

The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - 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 be from A to C?

- 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. - 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 - 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 '.

- Circumscribed 83357

Calculate the radius of the circle of the circumscribed triangle, which has side dimensions of 8, 10, and 14 cm. - 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.

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