Perimeter

Right triangle

Right triangle

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle).

The relation between the sides and angles of a right triangle is the basis for trigonometry.

The side opposite the right angle is called the hypotenuse (side c in the figure). The sides adjacent to the right angle are called legs (or catheti, singular: cathetus). Side a may be identified as the side adjacent to angle B and opposed to (or opposite) angle A, while side b is the side adjacent to angle A and opposed to angle B.

If the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple.

Video: Pythagorean theorem 3 | Right triangles and trigonometry

Principal properties

Area

As with any triangle, the area is equal to one half the base multiplied by the corresponding height. In a right triangle, if one leg is taken as the base then the other is height, so the area of a right triangle is one half the product of the two legs. As a formula the area T is

where a and b are the legs of the triangle.

Video: How to find the area of a right angled triangle

Altitudes

Altitude of a right triangle

If an altitude is drawn from the vertex with the right angle to the hypotenuse then the triangle is divided into two smaller triangles which are both similar to the original and therefore similar to each other. From this:

  • The altitude to the hypotenuse is the geometric mean (mean proportional) of the two segments of the hypotenuse.
  • Each leg of the triangle is the mean proportional of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

Video: How to Find the Altitude of a Right Triangle

In equations,

 (this is sometimes known as the right triangle ......

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Perimeter

Perimeter

A perimeter is a path that surrounds a two-dimensional shape. The term may be used either for the path or its length—it can be thought of as the length of the outline of a shape. The perimeter of a circle or ellipse is called its circumference.

Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter.

Formulas

shape formula variables
circle
where  is the radius of the circle and  is the diameter.
regular polygon
where  is the number of sides and  is the distance between center of the polygon and one of the vertices of the polygon.
equilateral polygon
where  is the number of sides and is the length of one of the sides.
rectangle
where is the length and is the width.
triangle
where , and are the lengths of the sides of the triangle.
square/rhombus
where is the side length.
general polygon
where is the length of the -th (1st, 2nd, 3rd ... nth) side of an n-sided polygon.

cardoid  
(drawing with )
 
 
 

The perimeter is the distance around a shape.

Video: What is a Perimeter in Math?

Polygons

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