# Heron's formula - practice problems - page 2 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: 61

- Determine 57151

The land has the shape of an obtuse triangle with sides of 40m, 30, and 60m. Determine the minimum mesh length for fencing and the land area in ares. - Triangle

Determine whether we can make a triangle with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201 - Circumference 43531

A triangle with a circumference of 69 cm has one side three times shorter than the longest of them and the other 3 cm shorter than the longest of them. Find the area of the triangle. - Annulus from triangle

Calculate the area of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm - The perimeter

The perimeter of a rhombus whose diagonal lengths are in the ratio 3:4 is 40 cm. What is its area in cm²? - Circle inscribed

There is a triangle ABC and a circle inscribed in this triangle with a radius of 15. 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? - Triangle ABC

Calculate the sides of triangle ABC with area 1404 cm², and if a: b: c = 12:7:18 - Calculate 81757

Calculate the size of the largest angle in triangle ABC if a = 7 cm, b = 8 cm, and c = 13 cm. Calculate the area of the triangle, the height per side a. - Second-longest 7659

The sides of the ABC triangle measure 39 cm, 42 cm, and 45 cm. The second-longest height of this triangle is 36 cm. What is its shortest height? - Triangle's 9731

Solve the triangle ABC if the side a = 52 cm, the height on the other side is vb = 21 cm, and the triangle's area is S = 330 cm². - Calculate triangle

In the triangle, ABC, calculate the sizes of all heights, angles, perimeters, and area if given a=40cm, b=57cm, and c=59cm. - Compute 4

Compute the exact value of the triangle area with sides 14 mi, 12 mi, and 12 mi long. - One trapezium

One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area. - 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 - The farmer

The farmer would like to first seed his small field. The required amount depends on the seed area. The field has a triangular shape. The farmer had a fenced field, so he knew the lengths of the sides: 119, 111, and 90 meters. Find a suitable way to determ - Parallelogram 64414

The parallelogram has side a = 58cm and diagonals u = 89cm, v = 52cm. Calculate the perimeter and area of this parallelogram. - 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?

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