# Heron's formula - practice problems

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: 67

- Triangular field

Find the area of a triangular field whose sides are 78m, 50m, and 112m. - Sides to area

If the sides of a triangle are 26 cm, 24 cm, and 10 cm, what is its area? - Triangle 8320

Is there a triangle with heights of 4, 7, and 10 meters? - Trapezoid - hard example

Bases of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter.

- A rhombus 2

A rhombus has sides of 170 meters and a diagonal of 300 meters. What is the area of the rhombus? - Diamond

The rhombus has a side 17 cm and one diagonal 22 cm long. Calculate its area. - Triangle SSS

Calculate the perimeter and area of a triangle ABC if a=40, b=35, and c=55. - Triangle 2668

The triangle ABC has side lengths a = 14 cm, b = 20 cm, c = 7.5 cm. Find the sizes of the angles and the area of this triangle. - 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

- Is right triangle or not

If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area. - Triangle

Calculate the triangle's heights ABC if the triangle's sides are a=26, b=81, and c=73. - Calculate 4424

Calculate the area of the triangle ABC if a = 10 cm, c = 8 cm, ta = 6 cm. - 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. - Triangle

The triangle has known all three sides: a=4.6 m, b=7.4 m, c= 3.8 m. Calculate the area of this triangle.

- Circles 2

Calculate the area bounded by the circumscribed and inscribed circle in a triangle with sides 16 cm, 20 cm, and 15 cm. - Inscribed 44101

A circle is inscribed in the triangle with sides of 13 cm, 14 cm, and 15 cm. What is its radius? - Sides of the triangle

Calculate triangle sides where its area is S = 84 cm² and a = x, b = x + 1, xc = x + 2 - Heron backlaw

Calculate the missing side in a triangle with sides 25 and 13 and area 152. - Sss triangle

Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm

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