# High school + Heron's formula - examples

- Triangle

Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles. - Triangle ABC

Calculate the sides of triangle ABC with area 1404 cm^{2}and if a: b: c = 12:7:18 - Described

Calculate perimeter of the circle described by a triangle with sides 478, 255, 352. - Trapezoid

Calculate area of trapezoid ABCD with sides |AD|= 57 cm, |DC|=30 cm, |CB|=7 cm, |AB|=40 cm.. - Triangle SSS

Calculate perimeter and area of a triangle ABC, if a=40, b=36 and c=36. - Cardboard box

We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we cal - Box

Cardboard box shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm and one diagonal 8 cm long and height of the box is 12 cm. The box will open at the top. How many cm^{2}of cardboard we need to cover overlap and joints that are 5% of ar - Heron backlaw

Calculate missing side in a triangle with sides 17 and 34 and area 275. - Park

In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m. - Circles 2

Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm. - Trapezoid - hard example

Base of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter. - 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 internal angles α = 15°28' and β = 45°. - Sails

We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail? - Sides of the triangle

Calculate triangle sides where its area is S = 84 cm^{2}and a = x, b = x + 1, xc = x + 2 - Four sides of trapezoid

Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area. - Triangle

The triangle has known all three sides: a=5.5 m, b=5.3 m, c= 7.8 m. Calculate area of this triangle. - Triangle

Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201 - The farmer

The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine th - Sides ratio

Calculate the circumference of a triangle with area 84 cm^{2}if a:b:c = 10:17:21 - Find the area

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft

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