Lesson 11.1

Areas of Parallelograms

Objectives

Find perimeters and areas of parallelograms.

Determine whether points on a coordinate plane define a parallelogram.

Areas of ParallelogramsA parallelogram is quadrilateral with both

pairs of opposite sides ll.Any side of the parallelogram can be

called a base. There is a corresponding altitude that is

perpendicular to each base.

If a parallelogram has an area of a square units, a base of b units, and a height of h units, then A = bh

Key Concept

Example 1:Find the Perimeter and Area of ACEG

AC = 28 Ft.AG = 15 Ft.

Use 45-45-90 to find the height of parallelogram ACEG.

To find the area substitute for A=bh.

The perimeter of ACEG = 86 feet Area= about 297

Example 2: Use area to solve a real-world problem.

RECREATION Blue Sky Water Park is having a new pool designed for their visitors. Find the total surfacearea of the water in the pool.To find the total surface area of the water, divide the pool into rectangles. Then find the area of each rectangle and add the areas to find the total area.

Rectangle 1:w = 15 m, l = 20 mRectangle 2:w = 45 - 20 - 10 or 15 m, l= 25 mRectangle 3:w = 10 m, l = 25 - 15 or 10 m

Rectangle 1A = lw

= 20 15= 300 m2

Rectangle 2A=lw

= 25 15= 375 m2

Rectangle 3A= lw

= 10 10= 100 m2

The total area is 775 m.

Example 3: Area on a Coordinate Plane

COORDINATE GEOMETRY The vertices of a quadrilateral are Q(-1, 4), R(2, 1),S(-1, -2), and T(-4, 1).

Assignment

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