Formulas for the Area of a Triangle

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What is the formula to find the area of a triangle using base and height?
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The formula is Area = (base × height) / 2.
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How can you find the area of a triangle using Heron's formula?
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Heron's formula is Area = √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2 and a, b, c are the lengths of the sides.
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What is the semi-perimeter in Heron’s formula?
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The semi-perimeter (s) is half the perimeter of the triangle, calculated as (a+b+c)/2.
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How do you calculate the area of an equilateral triangle?
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The area is calculated using the formula: Area = (√3/4) × side².
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What is a necessary condition to use the formula Area = 1/2 × base × height?
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You must know the base and the corresponding height (altitude) of the triangle.
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How is the area of a right triangle calculated?
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For a right triangle: Area = 1/2 × base × height, where base and height are the two perpendicular sides.
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Can the formula Area = 1/2 × base × height be used for any triangle?
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Yes, as long as the base and the corresponding height (perpendicular to the base) are known.
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How do you find the area of a triangle given vertices coordinates?
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Use the formula: Area = 1/2 × |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|.
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What is the formula for the area of a triangle that uses a circle's radius?
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The formula is Area = (abc)/(4R), where R is the circumcircle's radius.
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How can you find the area of a triangle using two sides and the included angle?
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Use the formula: Area = 1/2 × a × b × sin(C), where C is the included angle between sides a and b.
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What key information is needed to use Heron’s formula?
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The lengths of all three sides of the triangle.
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Why might Heron's formula be more practical in some cases?
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It is useful when the height of the triangle is not easily measurable but side lengths are known.
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For what type of triangle is Area = 1/2(absinC) used?
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This formula is used for scalene or any triangle where two sides and the included angle are known.
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How does the Pythagorean Theorem relate to finding the area of some triangles?
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For right triangles, Pythagorean Theorem helps find unknown side lengths needed to use the base-height formula.
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What does 'included angle' mean in the context of area formulas?
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An included angle is the angle formed between two known sides of a triangle.
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