Area of a Triangle Calculator
Need to find a triangle's area quickly? Our free calculator handles any triangle type! Just enter your known values base and height get instant results.
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About the Area of a Triangle
This is the formula for a triangle: base * height divided by two. Whatever the triangle is, whether it is an equilateral triangle, a scalene triangle, or a right-angled triangle—that is, whatever the triangle is, if we are given a base or a height in a triangle then we can calculate the area of any triangle by writing the values of all of them in this formula, no matter which triangle it is. So now we know what the base is and what the height is, okay? Because without understanding this, we cannot calculate the area of a triangle. So, look, the base is the length of one side of a triangle; we call it the base. A triangle has three sides, so whenever you are given a triangle, we call the bottom side the base. Now let's understand the height here. What is the height? You guys understand carefully that the base is the line that makes an angle of 90 degrees. That line is up to the top of the triangle; we call it the height.
The area of triangle 'ABC' is equal to base * height divided by two. So we will write 8 in place of the base and then 6 in place of the multiplied height. Now let's solve this: 8 × 6 = 48. Now we will divide 48 by two. What will be the result? 2 × 48 = 24. So the answer, which came out to be 24, will not be the same. So you people should know one rule: whenever you calculate the area of any area, use this metric of area. It always comes square; there are two components. In this, the base and height are in centimeters. Write centimeters here, then write two components on it. So this is the answer, which means it is necessary to write centimeters squared. If the height is 6 meters and the base is 8 meters, that is, both are meters, then we write meters here, and then divide them by two components. Okay, so in this way, the area of this triangle comes to be 24 centimeters square.
Area of a Triangle Calculation Formula
How can we calculate the area of the square here? Let us understand the process. The size of a rectangle is the same as the space inside it. It tells you how much area the square covers on a flat surface. You get it by using the length of the sides of the triangle and a simple formula.
You can use this handy chart to find the size of a rectangle:
The "base" is the bottom side, and the "height" is the distance from the base to the top corner. Just write these values into a formula, and you get an answer.
| Base & Height Formula: area = | | b × h |
|
Heron's Formula (3 sides): A = √s(s - a)(s - b)(s - c) where s = | |
|
SAS (2 sides & angle): A = | | ab sin (C) |
Area of a Triangle Calculation Example
1. Three Sides (SSS)
Use Heron's Formula when you know the lengths of all three sides a, b, and c.
Formula:
A= √s(s - a)(s - b)(s - c)
where s is the semi-perimeter:
Example:
Triangle with sides a = 3 cm, b = 4 cm, c = 5 cm.
Now we will calculate the semi-perimeter.
Apply Heron's formula:
Area = √6(6 - 3)(6 - 4)(6 - 5) = √6 × 3 × 2 × 1 = √36 = 36 cm2
Area = 36 cm 2
2. Two Sides and the Angle Between Them (SAS)
When you know two sides a and b and the angle C between them, use the trigonometric formula:
Formula:
Example:
Triangle with sides a = 5 cm, b = 6 cm, and included angle C = 30°.
Since sin (30°) = 0.5
A = 7.5 cm2
3. Two Angles and a Side Between Them (ASA)
When you know two angles (e.g., A and B) and the side between them (c), first find the third angle using the fact that the angles in a triangle sum to 180°. Then use the Law of Sines to find the other sides, followed by the area formula.
Steps:
Find the third angle: C = 180° - A - B.
Use the Law of Sines to find the other sides (if needed):
Use the area formula:
or, if you have side c, use:
|
Area = | | c2 × sin (A) × sin (B) | | | 2 × sin (C) |
| × a × b × sin (C) |
Example:
A triangle with angles A = 40°, B = 60°, and side c = 8 cm between them.
Find the third angle: C = 180° - 40° - 60° = 80°
Use the Law of Sines to find sides a and b:
Calculate a:
Calculate b:
Use the SAS area formula with sides a and b and angle C
| Area = |
|
× a × b × sin (C) = |
|
× 5.22 × 7.04 × sin 80° |
|
= | | × 5.22 × 7.04 × 0.9848 = 18.09 cm2 |
Alternatively, use the ASA-specific formula:
| Area = |
| c2 × sin (A) × sin (B) | | | 2 × sin(C) |
|
= |
| 82 × sin 40° × sin 60° | | | 2 × 80° |
|
|
= | | 64 × 0.6428 × 0.8660 | | | 2 × 0.9848 |
| = 18.09 cm2 |
Area = 18.09 cm².
FAQ
1. Is this Area of the Triangle calculator usable for every triangle?
Yes, as long as the base and height are known, the Area of a Triangle Calculator applies to any type of triangle. The theorem is true for scalene, isosceles, and equilateral triangles.
2. What measuring units are permissible?
Any standard measuring units are acceptable, such as meters, feet, inches, centimeters, etc. Square units, whichever is appropriate, will be used to indicate the answer.
3. For what reason is determining the area of the triangle important?
The area of a triangle is critical to a range of activities involving the quantity of materials needed for construction, land area, or other engineering calculations.
4. But what if I only know the triangle's side lengths?
In that scenario, you will need to use an alternative formula, such as Heron's formula, or use one of the specialized calculators to find the area by entering the side lengths.
5. How accurate is the area of a triangle calculator's area?
Depending on the data entered, the Area of a Triangle Calculator displays the precise findings without any further approximation. This feature makes it less prone to any mistakes that could possibly arise from hand calculation.
