You will need

- to know what the height and its properties
- - know what a right triangle
- to know what the hypotenuse is and sides,
- - be able to solve equations with one variable with parentheses

Instruction

1

If in a right triangle is known to at least one side and its height, to determine the area of a shape, multiply the height by the length of the side and divide the resulting number by two.

2

To compute the area

**of a triangle**with known height and known side first, find the height. For this we consider one of the equal right-angled triangles formed by the altitude.3

Side opposite the right angle is the hypotenuse, and the other two - legs. So, the height of the equilateral

**triangle**will be one of the smaller sides of the rectangular**triangle**. The second leg will be half the side of the large**triangle**, as the height of the right rectangle divides it in half, as a median.4

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, in order to know the height from the square of the hypotenuse (that is, from square one of the sides of an equilateral

**triangle**) subtract the square of the side formed by the half side of the equilateral**triangle**, and after that from the result of this calculation, extract the square root.5

Now when the height is known, find

**the area**of a shape by multiplying the height by the length of a side and dividing the resulting value by two.6

If you only know the height, then again consider one of the right triangles formed when carrying out height, which bisects the angle and side of a regular polygon. Based on the Pythagorean theorem, write down the equation a2 = c2-(1/2*s)2 where a2 is the height, c2 is the side of equilateral

**triangle**. In this equation find the value of the variable a.7

Knowing the height, calculate

**the area of**the right**triangle**. To do this, multiply the height of the side**of the triangle**and divide after multiplying the result in half.