2.  Find perimeters and areas of parallelograms.  Determine whether points on a coordinate plane define a parallelogram and then find its area.

3.  Recall, a parallelogram is a quadrilateral with both pairs of opposite sides ||.  Any side of a parallelogram can be called the base.  Each base has a corresponding altitude, a segment which is ┴ t o the base, called the height. height base

4.  If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh. Example 1 Base = 15 units Height = 12 units Area = 15 units x 12 units Area = 180 sq. units

5. Find the perimeter and area of the parallelogram.

6. Since opposite sides are equal, the perimeter would be equal to the following: 10 + 10 + 15 + 15 = 50 units

7. To find the area you must first find the height of the parallelogram. The triangle in the parallelogram is a 30º- 60º- 90º triangle. With this information we know that the shorter leg is equal to 1/2 of the hypotenuse or 1/2 (10) = 5. The longer leg, which is the height, is equal to the √3 times the length of the shorter leg. Therefore, the height is 5√3 or ≈ 8.7 units. The area is then = to the base, 15, times the height, 5√3. A= 15 5√3 A=129.9 units 2

8. A water park is having a new pool built. Find the total surface area of the pool. 15 m 20 m 45 m 10 m 25 m

9. 15 m 20 m 45 m 10 m 25 m First, divide the pool into three separate rectangles. 1 2 3 Then, find the lengths and widths (bases and heights) of each rectangle. Rectangle 1Rectangle 2Rectangle 3 L = 20 m, W = 15 mL = 25 m, W = 45 – 20 - 10 or 15 m L= 25 -15 or 10 m W= 10 m A = 20 x 15 A = 300 m ² A = 25 x 15 A = 375 m ² A= 10 x 10 A= 100 m ² Total Area= 300 + 375 + 100 or 775 m ²

10.  COORDINATE GEOMETRY The vertices of a quadrilateral are Q(-1, 4), R(2, 1), S(-1, -2), and T(-4, 1).  a.Determine whether the quadrilateral is a square, a rectangle, or a parallelogram.  b.Find the area of quadrilateral QRST. Q S T R

11. Slope of QR = = Slope of RS = = Slope of ST= = Slope of QT = = 4-1 -1-2 1-(-2) 2-(-1) -2-1 -1-(-4) 1-4 -4 –(-1) 3 -3 or -1 3 3 or 1 -3 3 or -1 -3 or 1 Q S T R Opposite sides have the same slope, so they are parallel. Also, the slopes of the consecutive sides are negative reciprocals of each other, so the sides are perpendicular. The quadrilateral is either a square or a rectangle. Determine whether quadrilateral QRST is a square, rectangle, or parallelogram.

12. Next, find the distance of the sides. QR = √(-1-2)² + (4-1)² = √18 or 3√2 ST = √[-4-(-1)]² + [1-(-2)]² RS = √[-2-(-1)]² + [1-(-2)]² = √18 or 3√2 QT = √[-4-(-1)]² + (1-4)² = √18 or 3√2 Since all sides have the same length, they are congruent and QRST is a square. Q S T R Let the base be RS and the height be ST. Since QRST is a square, all sides measure √18 units. A = bh A = √18 √18 A = 18 units 2

13. Pre-AP Pg. 598 #9 – 19, 20 – 28 evens Geometry Pg. 598 #3 – 5, 9 – 19, 28