Right Triangles – Guide About Area and Pythagorean Theorem

Right Triangles

Read the guide about “Right Triangles” with the complete explanation. A right triangle is a triangle with one angle equal to 90 degrees. It can be described in terms of its base, height, and hypotenuse. The sides of a right triangle perpendicular to each other are called the base and height, whereas the side opposite to the right angle is known as the hypotenuse.

The Greek mathematician Pythagoras discovered an interesting fact about the right triangles known as the Pythagorean theorem. In a right triangle, the sum of the squares of the lengths of each side of the triangle is equal to the square of the hypotenuse’s length. This property of a right triangle has many applications in the field of science, architecture, engineering, etc.

Pythagorean theorem is an important theorem used in geometry that shows the relationship between the lengths of the sides of a right-angled triangle. As the Pythagoras theorem holds great significance in geometry, gaining an in-depth understanding of this theorem forms the base for solving various mathematical problems in the field of construction, navigation, surveying, and architecture. Let’s take a look at what Pythagoras theorem is and how to find the area of a right triangle.

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What is Pythagoras Theorem?

Pythagoras theorem states that the sum of the square of the two sides of a right-angle triangle is equal to the square of the third side called the hypotenuse. The equation formed by the Pythagoras theorem is a^2 + b^2 = c^2, where a, b and c is the length of the sides of a right triangle. The ability to find the length of a side when the other two sides’ length is given makes the Pythagorean Theorem a beneficial construction and navigation technique.

By Applying the Universal Formula

The area of a right triangle can be found by applying the universal formula of the area of a triangle. That is, we can simply use the area of a triangle formula to calculate the area of a right triangle. Area = ½ x b x h, where ‘b’ and ‘h’ are the base length and the height of the triangle.

In a right triangle, we don’t require to find the height, unlike other triangles. Thus, we can multiply the length of two non-hypotenuse sides and halve the product to obtain the height.

Thus, if we can say that the area of the triangle ABC is A = ½ x b x c, where ‘c’ is the height of the right triangle.

Using HERON’s Formula

The heron’s formula can be applied to calculate the area of a right triangle without finding its height. If you know the value of all the sides of a triangle, you need not find the height to find the area. You can simply use the Heron formula as follows:

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Area =√(s) (s – a) (s – b)(s – c)

Where ‘s’ is the semi perimeter that can be defined as (a+b+c) / 2, a, b and c is the length of the sides of the right triangle.

Thus, if we know any two sides, we can easily find the area of the triangle using a combination of Pythagoras theorem and Heron formula or even the universal formula to measure the area of a right triangle.

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Right triangles are foundational in various fields of mathematics and other subjects like physics and geography. There are numerous ways kids can learn the concept of right triangles and the Pythagoras theorem. Cuemath offers excellent learning resources for kids to gain a clear understanding of various concepts and their applications in our everyday life. Its live online classes are designed to promote the real-life application of maths for kids to learn interestingly.

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By Sachan Lathiya

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