There are multiple different equations for calculating the area of a triangle, dependent on what information is known. If an equilateral triangle has an x for all sides, what is the area? We are told that the base is 9 and the height is 4 (remember that the height is the line that's perpendicular to the apex, or highest point, of the triangle and the base). In this case the SAS rule applies and the area can be calculated by solving (b x c x sinα) / 2 = (10 x 14 x sin(45)) / … To find the area of the triangle: Use the formula. Give your answer correct to 2 decimal places. Khan Academy has a nifty drag tool that lets you see how the area of a triangle is found using the rectangle/parallelogram it's inscribed in. This involves trigonometry. So how do you approach this problem to find the area of the triangle? Finding the area of a triangle can be tricky, even if you know the formula. The area of a polygon is the number of square units inside that polygon. Let’s look at an example. This formula may also be written like this: Here’s a diagram to help you envision this formula at play: This formula works for all types of triangles: With right triangles, the base and height are simply the two sides that form the right angle. You can find the area of a triangle by multiplying the base by the height and then dividing that number by 2. Once more, what this proves is that the area of a triangle will always equal half the area of the rectangle in which it is inscribed. The formula for the area of a triangle is A=1/2bh. What is the length of its base? (60° represents each of the angles in an equilateral triangle.) In other words, they're the two sides that connect to form a right angle. The best known and the simplest formula, which almost everybody remembers from school is: area = 0.5 * b * h, where b is the length of the base of the triangle, and h is the height/altitude of the triangle. How do I calculate the height of a triangle if I know the area and the base? For this, you’ll need to know the area of triangle formula. The 5 Strategies You Must Be Using to Improve 4+ ACT Points, How to Get a Perfect 36 ACT, by a Perfect Scorer. For example, if the base of your triangle is 5 cm and the height is 3 cm, you would calculate: You can also use this formula if you know one side length, plus the length of the hypotenuse. Try your hand at finding the area of a triangle with these three sample problems. To learn how to calculate the area of a triangle using the lengths of each side, read the article! Now, we finally have the height of our equilateral triangle (4√3): All that’s left to do is plug the base (8) and height (4√3) into our area of triangle formula: \$A=1/2bh\$\$A=1/2(8)(4√3)\$\$A=4(4√3)\$\$A=16√3\$. Base = b = 20. Check out our top-rated graduate blogs here: © PrepScholar 2013-2018. The area of the triangle is given by the formula mentioned below: Area of a Triangle = A = ½ (b × h) square units; where b and h are the base and height of the triangle, respectively. Without more information, you can't find an exact value. Solve for the value of the area. The height is found by multiplying the length of a side (x) by half the tangent of 60°. The College Entrance Examination BoardTM does not endorse, nor is it affiliated in any way with the owner or any content of this site. Double the area, then divide by the base. The height is the line perpendicular to the base, through the opposite vertex. wikiHow's Content Management Team carefully monitors the work from our editorial staff to ensure that each article is backed by trusted research and meets our high quality standards. How can you figure out the area of a triangle? Say that you’ve been asked to find the area of the following triangle (not drawn to scale): Here, we're told that the base of our triangle is 5 and the height is 6. You can also write the formula as: ½ x base x height For example, if the hypotenuse of a triangle is side c, the height and base would be the other two sides (a and b). This example will show you how to read user inputs in C++ and how to do mathematical calculations.. Before moving to the program, let me quickly show you the mathematical formula to calculate the triangle area. The legs must be the sides that are equal, so you just square the length of one of the legs and divide by 2. It can often help to visualize the rectangle or parallelogram whose area is equal to double that of the triangle you’re analyzing. Note that none of these triangles are drawn to scale. In these cases you'll need to know more than just how to find the area of a triangle; you'll have to know the Pythagorean theorem. To calculate the area of a triangle, start by measuring 1 side of the triangle to get the triangle's base. There are several ways to find the area of a triangle. Numerous other formulas exist, however, for finding the area of a triangle, depending on what information you know. Find the area of a triangle where height = 5 cm and width = 8 cm. There’s no shame in refreshing your memory or getting help! In this, a is the length of one short side, b is the length of the other short side, and c is the length of the hypotenuse (that is, the longest side of a triangle). To find the area of a triangle, multiply the base by the height, and then divide by 2. For example, if you have a triangle with a base of 4cm and a height of 2cm, then you would have an area of 4cm squared because 4 times 2 equals 8, and 8 divided by 2 equals 4. Solution: Area of triangle PQR = 1/2 pr sin Q = 1/2 × 6.5 × 4.3 × sin 39˚ = 8.79 cm 2. As you can see, to find the area, just multiply the base by the height and divide the result by 2. Examples: find the area of a triangle. The area of this equilateral triangle is 16√3 square units. You should also start memorizing the most important SAT/ACT math formulas so you can ace the Math section. If you know the base and height, you can use the standard formula A = 1/2bh. Got other questions about math? Perpendicular means at right angles. We know ads can be annoying, but they’re what allow us to make all of wikiHow available for free. Show Answer. wikiHow's. As mentioned, we have a and c, so we just need to use this theorem to find b (or h in our original equilateral triangle). 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