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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.
Steps
Method 1
Method 1 of 4:Using the Base and Height

1Find 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.

2Set 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] X Research source }Advertisement

3Plug 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.
 For example, if the base of your triangle is 5 cm and the height is 3 cm, you would calculate:
So, the area of a triangle with a base of 5 cm and a height of 3 cm is 7.5 square centimeters.
 For example, if the base of your triangle is 5 cm and the height is 3 cm, you would calculate:

4Find 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.
 You can also use this formula if you know one side length, plus the length of the hypotenuse. The hypotenuse is the longest side of a right triangle and is opposite the right angle. Remember that you can find a missing side length of a right triangle using the Pythagorean Theorem ().
 For example, if the hypotenuse of a triangle is side c, the height and base would be the other two sides (a and b). If you know that the hypotenuse is 5 cm, and the base is 4 cm, use the Pythagorean theorem to find the height:
Now, you can plug the two perpendicular sides (a and b) into the area formula, substituting for the base and height:
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Method 2
Method 2 of 4:Using Side Lengths

1Calculate the semiperimeter of the triangle. The semiperimeter 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] X Research source }
 For example, if a triangle has three sides that are 5 cm, 4 cm, and 3 cm long, the semiperimeter is shown by:
 For example, if a triangle has three sides that are 5 cm, 4 cm, and 3 cm long, the semiperimeter is shown by:

2Set up Heron’s formula. The formula is , where is the semiperimeter of the triangle, and , , and are the side lengths of the triangle.^{[3] X Research source }

3Plug the semiperimeter and side lengths into the formula. Make sure you substitute the semiperimeter for each instance of in the formula.
 For example:
 For example:

4Calculate the values in parentheses. Subtract the length of each side from the semiperimeter. Then, multiply these three values together.
 For example:
 For example:

5Multiply the two values under the radical sign. Then, find their square root. This will give you the area of the triangle in square units.
 For example:
So, the area of the triangle is 6 square centimeters.
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Method 3
Method 3 of 4:Using One Side of an Equilateral Triangle

1Find 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] X Research source }
 For example, you might have a triangle with three sides that are 6 cm long.

2Set 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] X Research source }

3Plug the side length into the formula. Make sure you substitute for the variable , and then square the value.
 For example if the equilateral triangle has sides that are 6 cm long, you would calculate:
 For example if the equilateral triangle has sides that are 6 cm long, you would calculate:

4Multiply 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 .
 For example:
 For example:

5Divide the product by 4. This will give you the area of the triangle in square units.
 For example:
So, the area of an equilateral triangle with sides 6 cm long is about 15.59 square centimeters.
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Method 4
Method 4 of 4:Using Trigonometry

1Find the length of two adjacent sides and the included angle. Adjacent sides are two sides of a triangle that meet at a vertex.^{[6] X Research source } 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.

2Set 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] X Research source }

3Plug the side lengths into the formula. Make sure you substitute for the variables and . Multiply their values, then divide by 2.
 For example:
 For example:

4Plug 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.
 For example, the sine of a 123degree angle is .83867, so the formula will look like this:
 For example, the sine of a 123degree angle is .83867, so the formula will look like this:

5Multiply the two values. This will give you the area of the triangle in square units.
 For example:
.
So, the area of the triangle is about 14,530 square centimeters.
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Community Q&A

QuestionHow do I find the length and width of a triangle before calculating the area?Community AnswerIt 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.

QuestionHow can I calculate the area of an equilateral triangle?Community AnswerIf 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.

QuestionHow can I find the area of an isosceles right triangle?Community AnswerThe 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 11(square root of 2), you just divide the hypotenuse by sqrt(2), square what you get, and divide by 2.

QuestionIf an equilateral triangle has an x for all sides, what is the area?This involves trigonometry. You have to find the height of the triangle, which is the distance from one vertex to the opposite side. The height is found by multiplying the length of a side (x) by half the tangent of 60°. (60° represents each of the angles in an equilateral triangle.) Half the tangent of 60° is 0.866. Thus the height is 0.866x. Multiply that by x and divide by two to get the area.

QuestionA triangle has an area of 24 square units. Its height is 6 units. What is the length of its base?To find the base, double the area, then divide by the height.

QuestionA triangle has a base length of 2x+4 and a height of 3y; what is the area?Community AnswerWithout more information, you can't find an exact value. You can, however, state the height as the value of 1/2bh by plugging in these expressions for the base and height. So the area is 1/2(2x+4)(3y); (x+2)(3y); 3xy + 6y.

QuestionHow do I calculate the height of a triangle if I know the area and the base?Double the area, then divide by the base.

QuestionHow can I mark the center point of any type of triangle?Community AnswerTo find the centroid of a triangle, use the formula from the preceding section that locates a point twothirds of the distance from the vertex to the midpoint of the opposite side. For example: to find the centroid of a triangle with vertices at (0,0), (12,0) and (3,9), first find the midpoint of one of the sides.

QuestionIf the sides of a triangle are 14 cm, 11 cm, and 9 cm, and the height is 7 cm, what is the area?Community AnswerSince you know all three side lengths, you can use Heron's formula as described in this article. If you know which side functions as the base, you can use the formula A = 1/2bh

QuestionHow do I calculate area when two angles and one side have been given?Community AnswerAssuming your triangle is a right triangle, you can use trigonometry to find the other missing side lengths. Once you have all side lengths, you can use Heron's formula, as described in this article, to find the area. For more information on how to use trigonometry, you can read the following article: http://www.wikihow.com/UseRightAngledTrigonometry
Video
Tips
 If you're not exactly sure why the baseheight 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 nonright 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.Thanks!
References
 ↑ https://www.mathsisfun.com/algebra/trigareatrianglewithoutrightangle.html
 ↑ http://mathworld.wolfram.com/Semiperimeter.html
 ↑ http://mathworld.wolfram.com/HeronsFormula.html
 ↑ http://www.mathopenref.com/equilateral.html
 ↑ http://www.mathwords.com/a/area_equilateral_triangle.htm
 ↑ http://www.mathopenref.com/adjacentsides.html
 ↑ https://www.mathsisfun.com/algebra/trigareatrianglewithoutrightangle.html
About This Article
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!