Area of a Triangle ExplainedDate: 06/17/99 at 01:03:35 From: Tracy Watson Subject: Finding area of triangle Dear Dr. Math, I am a homeschool mother in need of a little help on how to explain how to find the value of A, when the area = 48 and B = 8. The formula we are using is as follows: A = (1/2)ab I can look in the teacher key and see how to work the problem but I don't know how to explain it to him. Please help if you can! Thanks, Tracy Watson Date: 06/17/99 at 01:33:55 From: Doctor Jeremiah Subject: Re: Finding area of triangle Hi Tracy, The formula for the area of a triangle is Area = 1/2 * a * b where "a" is the height and "b" is the width of the base. + --- / \ | / \ | / \ a / \ | / \ | +-----------+ --- |-----b-----| It doesn't matter whether the triangle is right angled or not (but it is easier to explain if it is right angled.) Here is how I would explain it with a right triangle: Think about the area of a rectangle... +-----+ --- | | | | | | | | a | | | | | | +-----+ --- |--b--| RectangleArea = a * b Now split it up into two triangles... +-----+ --- | /| | | / | | | / | a | / | | |/ | | +-----+ --- |--b--| Two triangles fit into the same area so RectangleArea = 2 * TriangleArea And then if we combine these two equations... RectangleArea = a * b <== RectangleArea = 2 * TriangleArea 2 * TriangleArea = a * b Then multiply both sides by 1/2 ... 2 * TriangleArea = a * b 1/2 * 2 * TriangleArea = 1/2 * a * b TriangleArea = 1/2 * a * b And there we have the equation for the area of a triangle. To explain triangles that do not have a right angle: + --- / \ | / \ | / \ a / \ | / \ | +-----------+ --- |-----b-----| First split the triangle up into two right triangles... + --- /|\ | / | \ | / | \ a / | \ | / | \ | +-----+-----+ --- |--c--| |-----b-----| The Area of the triangle on the left is LeftTriangleArea = 1/2 * a * c The Area of the triangle on the right is RightTriangleArea = 1/2 * a * (b-c) The area of the whole thing is TriangleArea = LeftTriangleArea + RightTriangleArea TriangleArea = (1/2 * a * c) + (1/2 * a * (b-c)) Now factor out the "1/2 * a" ... TriangleArea = (1/2 * a * c) + (1/2 * a * (b-c)) TriangleArea = 1/2 * a * (c) + 1/2 * a * (b-c) TriangleArea = 1/2 * a * (c + b-c) And simplify... TriangleArea = 1/2 * a * (c + b-c) TriangleArea = 1/2 * a * b Let me know if this helps. - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/ |
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