How do i find the area of a triangle

#1/2bh# where #b# is the base and #h# is the height.

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What are the 3 formulas for the area of a triangle?
What is a formula of a triangle?

Explanation:

Multiply the base of the triangle by the height of the triangle by #1/2#. To understand this formula, I'll explain where it comes from. Two triangles put together make a square or parallelogram, which to find the area of you just multiply the base by the height. Since a triangle is half a square or parallelogram, you multiply by #1/2#.

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The most common way to find the area of a triangle is to take half of the base times the height. Numerous other formulas exist, however, for finding the area of a triangle, depending on what information you know. Using information about the sides and angles of a triangle, it is possible to calculate the area without knowing the height.

1
Find the base and height of the triangle. The base is one side of the triangle. The height is the measure of the tallest point on a triangle. It is found by drawing a perpendicular line from the base to the opposite vertex. This information should be given to you, or you should be able to measure the lengths.
- For example, you might have a triangle with a base measuring 5 cm long, and a height measuring 3 cm long.
2
Set up the formula for the area of a triangle. The formula is , where is the length of the triangle’s base, and is the height of the triangle.[1]
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3
Plug the base and height into the formula. Multiply the two values together, then multiply their product by . This will give you the area of the triangle in square units.
4

Find the area of a right triangle. Since two sides of a right triangle are perpendicular, one of the perpendicular sides will be the height of the triangle. The other side will be the base. So, even if the height and/or base is unstated, you are given them if you know the side lengths. Thus you can use the formula to find the area.

1

Calculate the semiperimeter of the triangle. The semi-perimeter of a figure is equal to half its perimeter. To find the semiperimeter, first calculate the perimeter of a triangle by adding up the length of its three sides. Then, multiply by .[2]
2
Set up Heron’s formula. The formula is , where is the semiperimeter of the triangle, and , , and are the side lengths of the triangle.[3]
3

Plug the semiperimeter and side lengths into the formula. Make sure you substitute the semiperimeter for each instance of in the formula.
4
Calculate the values in parentheses. Subtract the length of each side from the semiperimeter. Then, multiply these three values together.
5
Multiply the two values under the radical sign. Then, find their square root. This will give you the area of the triangle in square units.

1

Find the length of one side of the triangle. An equilateral triangle has three equal side lengths and three equal angle measurements, so if you know the length of one side, you know the length of all three sides.[4]
- For example, you might have a triangle with three sides that are 6 cm long.
2
Set up the formula for the area of an equilateral triangle. The formula is , where equals the length of one side of the equilateral triangle.[5]
3
Plug the side length into the formula. Make sure you substitute for the variable , and then square the value.
4
Multiply the square by . It’s best to use the square root function on your calculator for a more precise answer. Otherwise, you can use 1.732 for the rounded value of .
5
Divide the product by 4. This will give you the area of the triangle in square units.

1
Find the length of two adjacent sides and the included angle. Adjacent sides are two sides of a triangle that meet at a vertex.[6] The included angle is the angle between these two sides.
- For example, you might have a triangle with two adjacent sides measuring 150 cm and 231 cm in length. The angle between them is 123 degrees.
2
Set up the trigonometry formula for the area of a triangle. The formula is , where and are the adjacent sides of the triangle, and is the angle between them.[7]
3
Plug the side lengths into the formula. Make sure you substitute for the variables and . Multiply their values, then divide by 2.
4
Plug the sine of the angle into the formula. You can find the sine using a scientific calculator by typing in the angle measurement then hitting the "SIN" button.
5
Multiply the two values. This will give you the area of the triangle in square units.

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Question
How do I find the length and width of a triangle before calculating the area?

It should be included in the problem. If it is a right triangle, use the Pythagorean Theorem (A squared + B squared = C squared) to find the missing side.
Question
How can I calculate the area of an equilateral triangle?

If you know the base and height, you can use the standard formula A = 1/2bh. If you know the three side lengths, you can use the method for equilateral triangles described in this article.
Question

How can I find the area of an isosceles right triangle?

The legs must be the sides that are equal, so you just square the length of one of the legs and divide by 2. If you only have the hypotenuse: since isosceles right triangles come in the ratio 1-1-(square root of 2), you just divide the hypotenuse by sqrt(2), square what you get, and divide by 2.

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If you're not exactly sure why the base-height formula works this way, here's a quick explanation. If you make a second, identical triangle and fit the two copies together, it will either form a rectangle (two right triangles) or a parallelogram (two non-right triangles). To find the area of a rectangle or parallelogram, simply multiply base by height. Since a triangle is half of a rectangle or parallelogram, you must therefore solve for half of base times height.

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To calculate the area of a triangle, start by measuring 1 side of the triangle to get the triangle's base. Then, measure the height of the triangle by measuring from the center of the base to the point directly across from it. Once you have the triangle's height and base, plug them into the formula: area = 1/2(bh), where "b" is the base and "h" is the height. To learn how to calculate the area of a triangle using the lengths of each side, read the article!

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What are the 3 formulas for the area of a triangle?

Area of triangle = 1/2 × side 1 × side 2 × sin(θ); when 2 sides and the included angle is known, where θ is the angle between the given two sides. Area of an equilateral triangle = (√3)/4 × side. Area of an isosceles triangle = 1/4 × b√4a2−b2 4 a 2 − b 2 ; where 'b' is the base and 'a' is the length of an equal side.

What is a formula of a triangle?

The law of cosines generalizes the Pythagorean formula to all triangles. It says that c², the square of one side of the triangle, is equal to a² + b², the sum of the squares of the the other two sides, minus 2ab cos C, twice their product times the cosine of the opposite angle.