![]() As the area of a right triangle is equal to a × b / 2, then. c a / sin () b / sin (), explained in our law of sines calculator. ![]() ![]() Take a square root of sum of squares: c (a² + b²) Given an angle and one leg. Let's start with the trigonometric triangle area formula:Īrea = (1/2) × a × b × sin(γ), where γ is the angle between the sides. Use the Pythagorean theorem to calculate the hypotenuse from the right triangle sides. Substituting h into the first area formula, we obtain the equation for the equilateral triangle area: One leg of that right triangle is equal to height, another leg is half of the side, and the hypotenuse is the equilateral triangle side.Īfter simple transformations, we get a formula for the height of the equilateral triangle: See our right triangle calculator to learn more about right triangles. It depends on the data youre given as to how to proceed to determine both the lateral. The most general formula for the surface area of any prism is: Total area Lateral area + 2 × Base area. ![]() Height of the equilateral triangle is derived by splitting the equilateral triangle into two right triangles. The total surface area of a triangular prism is the sum of the areas of all its faces: the three lateral faces (rectangles) and two bases (triangles). The basic formula for triangle area is side a (base) times the height h, divided by 2: H = a × √3 / 2, where a is a side of the triangle.īut do you know where the formulas come from? You can find them in at least two ways: deriving from the Pythagorean theorem (discussed in our Pythagorean theorem calculator) or using trigonometry. The formula for a regular triangle area is equal to the squared side times the square root of 3 divided by 4:Īnd the equation for the height of an equilateral triangle looks as follows: ![]()
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