Equilateral call the triangle having three equal parties and three identical corners. Such triangle is called still correct. Height which is carried out from top to the basis at the same time is a bisector and a median what follows from that this line divides a top corner into two equal corners, and the basis by which falls, into two equal pieces. These properties of a triangle will help to calculate its square equal to a half of the work of height at any of its parties.
It is required to you
- - know what is height and its properties
- - know what is a rectangular triangle
- - know what is a hypotenuse and legs
- - to be able to solve the equations from one variable with brackets
Instruction
1. If in the correct triangle there are at least one known party and its height, then for determination of the area of a figure increase height by length of the party and divide the turned-out number into two.
2. For calculation of the area of a triangle with an unknown height and the known party at first find height. For this purpose consider one of the equal rectangular triangles formed by height.
3. The party, opposite to a right angle, will be a hypotenuse, and two others - legs. Means, height of an equilateral triangle will be one of legs of a smaller rectangular triangle. The second leg will equal to a half of the party of a big triangle as height in the correct rectangle halves it, being a median.
4. According to Pythagorean theorem, the square of a hypotenuse is equal to the sum of squares of legs. Therefore to learn height, from a hypotenuse square (that is) subtract a square of the leg formed by a half of the party of an equilateral triangle from a square of one of the parties of an equilateral triangle then surely take a square root from result of this calculation.
5. Now, when height is known, find the area of a figure, having increased height by length of the party and having divided the turned-out value into two.
6. In case only height is known to you, then again consider one of the rectangular triangles which are formed when carrying out height which halves a corner and the party of a regular polygon. Leaning on Pythagorean theorem, work out an equation² = with²-(1/2*с)² where a² - height, with² - the party of an equilateral triangle. Find value of variable a in this equation.
7. Having learned height, calculate the area of the correct triangle. For this purpose increase height by the party of a triangle and halve the result received after multiplication.