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Chapter 9 Area

Matt Cashel & Stephen Woo. Chapter 9 Area. Lesson 1: Area. A polygon. A polygonal region. The Area Postulate: Every polygonal regional has a positive number called its area such that Congruent triangles have equal areas

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Chapter 9 Area

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  1. Matt Cashel & Stephen Woo Chapter 9Area

  2. Lesson 1: Area A polygon A polygonal region The Area Postulate: Every polygonal regional has a positive number called its area such that Congruent triangles have equal areas The area of a polygonal region is equal to the sum of the areas of its not overlapping parts

  3. Lesson 2: Squares and Rectangles H Altitude (height) Rectangle B Base The area of a rectangle is the product of its base and altitude. A = B×H

  4. Lesson 2: Squares and Rectangles The area of a square is the square of its side. A = S×S S Side Square S Side

  5. Lesson 3: Triangles The area of a right triangle is half the product of its legs. A = ½ ab B a Area of a triangle is half the product of any base and corresponding altitude Right Triangle A C b Altitude: It refers to a perpendicular line segment from a vertex to the line of the opposite side.

  6. F Y C Obtuse Triangle E D X Y Triangles with equal bases and equal altitudes have equal areas. Scalene Triangle B A X

  7. Lesson 4: Parallelograms and Trapezoids • The area of a parallelogram is the product of any base and corresponding altitude • The area of a Trapezoid is half the product of its altitude and the sum of its bases

  8. Altitude: The altitude of a quadrilateral is the distance between two parallel lines if it has any

  9. Lesson 5: The Pythagorean Theorem • The square of the Hypotenuse of a right triangle is equal to the sum of the squares of its legs • If the square of one side of a triangle is equal to the sum of the squares of the other two sides, the triangle is a right triangle

  10. Simplifying Radicals • Radicand- Term under radical sign • You can only add rads with the same radicand • You can multiply any radicals • A radical expression is simplified if: • All parenthesis have been multiplied as indicated • No radicand contains perfect squares as factors • No terms contain a radicand the same as another term.

  11. Heron’s Theorem A theorem used to find the area of any triangle. √s(s-a)(s-b)(s-c) while s= (a+b+c)/2 a b c Equilateral triangles: d=e=f Area formula of equilateral triangle: a2√3/4 e d f

  12. Chapter 9 Summary • The formulas in this chapter is useful to find areas of quadrilaterals and any triangles. These formulas are useful in next chapters that involve finding the surface areas of 3 dimensional figures. • Simplifying radicals in equations is useful when finding the exact form.

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