Where to find triangles

When none of the sides of a triangle have equal lengths, it is referred to as scalene, as depicted below. Tick marks on the edge of a triangle are a common notation that reflects the length of the side, where the same number of ticks means equal length.

Similar notation exists for the internal angles of a triangle, denoted by differing numbers of concentric arcs located at the triangle's vertices. As can be seen from the triangles above, the length and internal angles of a triangle are directly related, so it makes sense that an equilateral triangle has three equal internal angles, and three equal length sides.

Note that the triangle provided in the calculator is not shown to scale; while it looks equilateral and has angle markings that typically would be read as equal , it is not necessarily equilateral and is simply a representation of a triangle. When actual values are entered, the calculator output will reflect what the shape of the input triangle should look like. Triangles classified based on their internal angles fall into two categories: right or oblique.

The longest edge of a right triangle, which is the edge opposite the right angle, is called the hypotenuse. Any triangle that is not a right triangle is classified as an oblique triangle and can either be obtuse or acute. There are multiple different equations for calculating the area of a triangle, dependent on what information is known.

Likely the most commonly known equation for calculating the area of a triangle involves its base, b , and height, h. The "base" refers to any side of the triangle where the height is represented by the length of the line segment drawn from the vertex opposite the base, to a point on the base that forms a perpendicular. Given the length of two sides and the angle between them, the following formula can be used to determine the area of the triangle.

We can use this to our advantage by once again, substituting the area formula:. To find h, we visualize the equilateral triangle as two smaller right triangles, where the hypotenuse is the same length as the side length b. By the rule , a special case of a right triangle, we know that the base of this smaller right triangle is and the height of this smaller right triangle is , assuming b to be the hypotenuse.

And substitute for the height:. As you can see, the base of a triangle can be calculated through many different ways depending on the type of triangle and information you have.

However, the length of the base is always related to the area of the triangle with the area formula. The Pythagorean Theorem can help you out if you are working with right triangles. To use the site, please enable JavaScript in your browser and reload the page.

Trigonometric functions are also used to find the area of a triangle when we know two sides and the angle formed between them. Triangles can be classified based on their angles as acute, obtuse, or right triangles.

They can be scalene, isosceles, or equilateral when classified based on their sides. Heron's formula is used to find the area of a triangle when the length of the 3 sides of the triangle is known. To use this formula, we need to know the perimeter of the triangle which is the distance covered around the triangle and is calculated by adding the length of all three sides.

Consider the triangle ABC with side lengths a, b, and c. To find the area of the triangle we use Heron's formula:. When two sides and the included angle of a triangle are given, we use a formula that has three variations according to the given dimensions. For example, consider the triangle given below. When sides 'b' and 'c' and included angle A is known, the area of the triangle is:.

When sides 'a' and 'b' and included angle C is known, the area of the triangle is:. When sides 'a' and 'c' and included angle B is known, the area of the triangle is:. The area formulas for all the different types of triangles like the equilateral triangle, right-angled triangle, and isosceles triangle are given below.

Therefore, the height of the triangle is the length of the perpendicular side. An equilateral triangle is a triangle where all the sides are equal. The perpendicular drawn from the vertex of the triangle to the base divides the base into two equal parts.

To calculate the area of the equilateral triangle, we need to know the measurement of its sides. An isosceles triangle has two of its sides equal and the angles opposite the equal sides are also equal.