Isosceles triangle refers to the polygon composed of two equal opposing sides. Meanwhile, the area of an isosceles triangle is the space covered by the three edges and three vertices in two-dimensional space. The area of a right isosceles triangle formula, i.e. (1/2) × Base × Height square units, helps us calculate the mathematical problem easily.
What is the Area Of A Isosceles Triangle:
The area of an isosceles triangle is defined as the total two-dimensional space enclosed by three sides of the triangle. The triangle comprises a 90º angle and two 45° angles that are acute and congruent.
We can find the area in square units by the general rule of mathematics. Likewise, we can measure the area of the isosceles triangle if we know its height and base measurements, where the triangle’s height is the distance from the base to the opposing vertex.
Learn how much room a triangle with an isosceles angle occupies by finding its area; this knowledge helps solve several mathematics and geometric difficulties.
Here are the essential properties of Isosceles right angle triangle:
- It has two sides of equal length
- The two-dimensional space has one right angle, i.e., 90 degree
- The two sides of this triangle, the base and the height, are at right angles.
- An isosceles right triangle has two additional angles, each measuring 45 degrees, and they are acute and congruent with each other.
- An isosceles triangle always has a total of three interior angles that are equal to 180 degrees.
Formula To Calculate Isosceles Triangle Formula:
If you want to calculate the formula of an isosceles triangle, you can use the below-mentioned formula. All you need to do is get some measurements. You can easily calculate its area if the base and height measurements are given.
Here is the formula to get the area of an isosceles triangle:
Area = ½ × base × Height
Area of A Right Isosceles Triangle Formula:
Though fantastic, our isosceles triangle area calculator won’t be required for any exams. Alright, then, let’s find out what an isosceles triangle’s area is. As with any other triangle, the area formula applies to isosceles triangles as well:
Area = ½ × b × H
where,
- A = area of the isosceles triangle;
- b = base side’s length, and
- h = triangle’s height.
As we can see in the above formula, height, and base measurements are required to get the area. But in some cases, the height has yet to be discovered. How will it calculate its area without a given height? DONT FRET! We have got you covered.
Depending on the available facts, one may apply one of many formulae to get the area of a isosceles triangle. An isosceles triangle’s area may be calculated using various methods, including angles, height-free sides, and so on.
A few of the most used formulas for the area of the isosceles triangle are listed below:
- Apply A = ½ × b × h if the base and height of the triangle are given
- If all three measurements of the triangle are known, then use A = ½[√(a2 − b2 ⁄4) × b]
- When you already know the angle between two sides and the length of both sides, then use A = ½ × b × c × sin(α)
Have a look at the table for a better understanding of the area of a isosceles triangle:
Given Parameters of Isosceles Triangle | Formula to Calculate Area (in square units) |
Base and height | A=(12)×(b)×(h) |
All three sides are known | A = ½[√(a2 − b2 ⁄4) × b] |
Length of 2 two sides and an angle between them | A=12×b×a×sin(α) |
Two angles and length between them | A=[a2×sin(β2)×sin(α)] |
Isosceles right triangle | A=12×a2 |
How To Find Area of Isosceles Triangle Formula using Sides:
In a few cases, you know the measurements of an isosceles triangle’s side length and base. These situations help you calculate its altitude. Here is the formula to find the area of the isosceles triangle using sides:
A = ½[√(a2 − b2 ⁄4) × b], where b is the base, and a is the length of two equal sides.
Derivation Of Area of Isosceles Triangle Formula using Sides:
The isosceles triangle has a base length of “b” units and equal-length sides; hence, the length of the triangle is “a” units. As we can see in the figure, the base of an isosceles triangle is divided into two halves from the center.
Following the above figure ABC, we have
BD=DC=12×BC=12×b (
AB=AC=a
Now, we will apply Pythagoras’ theorem:
AB2=BD2+AD2
- a2=(b2)2+(AD)2
- AD =[√(a2 − b2 ⁄4)
Hence proved the height of the triangle is [√(a2 − b2 ⁄4)
As we know, the general formula to calculate the area of an isosceles triangle is:
Area=(12)×(b)×(h)
When we put the height value into the standard equation for the isosceles triangle’s area, we obtain:
The surface area of an isosceles triangle with two sides:
A = ½[√(a2 − b2 ⁄4) × b]
Equilateral Triangle – Area Of An Equilateral Triangle Calculator
Equilateral triangles are composed of regular polygons with three equal sides. When we dissect the term “equilateral,” we find that “equi” means “equivalent” and “lateral” means “sides.” This equiangular triangle, also known as regular polygons, has a value of 60 degrees.
The area covered inside this regular polygon perimeter refers to the area of an equilateral triangle. With each congruent interior angle, the midpoint, angle bisector, and height of a right triangle are identical on each side.
If you want to calculate the area of the equilateral triangle, you can figure it in one of two ways: by measuring the height or by reading the side length of a two-dimensional space.
Formula by using the length of the sides:
Area = (a² × √3)/ 4
Here, “a” is the length of sides.
Formula by using the Height:
h = a × √3 / 2
where “h” is the height of the triangle.
Conclusion:
The area of an isosceles triangle is the area enclosed by a two-dimensional space. This triangle has two equal sides, which are right angles to each other. Hence, the sum of all the inner angles becomes 180. To calculate the area of an isosceles triangle, you must know the base and height of the triangle. In this article, we have mentioned all the other formulas to find the surface area of the isosceles triangle.