8.1 Area of Rectangles and Parallelograms When you add to the truth you subtract from it. The Talmud.

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Presentation transcript:

8.1 Area of Rectangles and Parallelograms When you add to the truth you subtract from it. The Talmud

Objectives Develop the concept of area Derive formulas for the areas of a: – Rectangle – Parallelogram – Triangles – Trapezoids – Kites Apply area formulas to solve problems

1.Look at the parallelogram on your table. 2.Find the area of the figure in as many ways as possible. Activity

We can use other shapes to help is find the area of a parallelogram. Rectangle Area Conjecture The area of a rectangle is given by the formula _____________ where A is the area, b is the length of the base, and h is the height of the rectangle. A = b * h

Investigation: Area Formula for Parallelograms p. 412 Investigate! Parallelogram Area Conjecture: The area of a parallelogram is given by the formula ___________, where A is the area, b is the length of the base, and h is the height of the parallelogram. A = b* h

8.2 Areas of Triangles, Trapezoids, and Kites Investigation 1: Area Formula for Triangles p.417 Investigation 2: Area Formula for Trapezoids p. 417 Investigation 3: Area Formula for Kites p. 418 Triangle Area Conjecture The area of a triangle is given by the formula _____________, where A is the area, b is the length of the base, and h is the height of the triangle. Trapezoid Area Conjecture The area of a trapezoid is given by the formula __________________, where A is the area, b 1 and b 2 are the lengths of the two bases, and h is the height of the trapezoid. Kite Area Conjecture The area of a kite is given by the formula ________________. A = ½ * b * h A = ½ * (b 1 + b 2 ) * h A = ½ * d 1 * d 2

What some were are discoveries? Every triangle is half a parallelogram with the same base and height. Every trapezoid is half a parallelogram whose base is the sum of the bases of a trapezoid and whose height is the same as a trapezoid. Every kite is half a rectangle whose base and height are the kite’s diagonals.