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Find perimeters and areas ofparallelograms.

Determine whether points on acoordinate plane define aparallelogram and then find its area.

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Recall, a parallelogram is a quadrilateralwith 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 to the base, called the

height..

height

base

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If a parallelogram has an area ofAsquare units, a base of bunits, and a

height ofhunits, thenA = bh.Example 1

Base = 15 units

Height = 12 unitsArea = 15 units x 12 units

Area = 180 sq. units

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Find the perimeter and area of theparallelogram.

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Since opposite sides are equal, theperimeter would be equal to thefollowing:

10 + 10 + 15 + 15 = 50 units

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To find the area you must first findthe height of the parallelogram.

The triangle in the parallelogram isa 30- 60- 90 triangle. With thisinformation we know that theshorter leg is equal to 1/2 of thehypotenuse or 1/2 (10) = 5.

The longer leg, which is the height,is equal to the 3 times the lengthof the shorter leg. Therefore, theheight is 53 or 8.7 units.

The area is then = to the base,15, times the height, 53.

A= 15 53A=129.9 units2

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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

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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 1 Rectangle 2 Rectangle 3

L = 20 m, W = 15 m L = 25 m,W = 4520 - 10 or 15 m

L= 25 -15 or 10 mW= 10 m

A = 20 x 15A = 300 m

A = 25 x 15A = 375 m

A= 10 x 10A= 100 m

Total Area= 300 + 375 + 100 or 775 m

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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 asquare, arectangle, ora parallelogram.

b. Find the area of quadrilateral QRST.

Q

S

T R

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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

-3or -1

3

3or 1

-3

3or -1

-3

- 3or 1

Q

S

T R

Opposite sides have the sameslope, so they are parallel. Also,the slopes of the consecutivesides are negative reciprocals ofeach other, so the sides areperpendicular. The quadrilateralis either a square or a rectangle.

Determine whether quadrilateral QRSTis asquare,rectangle, orparallelogram.

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Next, find the distance of the sides.

QR= (-1-2) + (4-1)

= 18 or 32

ST= [-4-(-1)] + [1-(-2)]

RS= [-2-(-1)] + [1-(-2)]= 18 or 32

QT= [-4-(-1)] + (1-4)

= 18 or 32

= 18 or 32

Since all sides have the same length,they are congruent and QRSTis asquare.

Q

S

T R

Let the base be RSand the height be ST. Since QRSTis a square, allsides measure 18 units.

A = bh

A= 18 18

A= 18 units2

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