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 ConjectureThe 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 Trianglesp.417

Investigation 2: Area Formula for Trapezoidsp. 417

Investigation 3: Area Formula for Kitesp. 418

Triangle Area ConjectureThe 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 ConjectureThe area of a trapezoid is given by the formula __________________, where A is the area, b1 and b2 are the lengths of the two bases, and h is the height of the trapezoid.

Kite Area ConjectureThe area of a kite is given by the formula ________________.

A = ½ * b * h

A = ½ * (b1+ b2) * h

A = ½ * d1 * d2

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.