18.2 Polygons

A polygon is a flat closed figure described by straight-line segments

and angles.

• Polygons are named by the number of sides they contain and other relations.

• The base of any polygon is the horizontal side or a side that would be horizontal if the polygon’s orientation is modified.

• The adjacent side is the side that has an endpoint in common with the base.

The kinds of polygons we will work with will be quadrilaterals and

triangles. We will use formulas to find both perimeter and area of

these shapes.

The following are quadrilaterals for which you need to be able to

calculate the perimeter and area:

• Parallelogram- opposite sides are parallel

• A = bh

• P = 2(a + b)

a

b

hBase and heightalways form right angles

The following are quadrilaterals for which you need to be able to

calculate the perimeter and area:• Rectangle- a parallelogram with 4 right

angles.

• A = bh or lw• P = 2(b + h) or 2(l + w)

b

h

The following are quadrilaterals for which you need to be able to

calculate the perimeter and area:

• Square- a rectangle with 4 equal sides

• A =

• P = 4b or 4s

2 2 or sb

b

The following are quadrilaterals for which you need to be able to

calculate the perimeter and area:

• Rhombus- a parallelogram with 4 equal sides

• A= bh• P = 4b

bh

b

The following are quadrilaterals for which you need to be able to

calculate the perimeter and area:

• Trapezoid- a quadrilateral with one pair of parallel sides.

• A = ½ (a + b)h• P = a + b + c + d

a

b

c dh

The area of a rectangle is 280 sq cm. Its width is 14 cm. Find its

length.

A 150 sq/ft roll of fiberglass is 30 in wide. What is its length in feet?

If the cost is $9.75/sq yd, what is the cost of the roll?

Find the area.

2168 ft

248 ft

20 ft

12 ft

14 ft6 ft

8 ft

2168 48 216 ft

The replacement cost for construction of the building below is $75/sq.ft.

Determine how much insurance should be carried for full replacement.

226 44 1144 ft

224 40 960 ft

228 25 700 ft

75 ft

40 ft

24 ft

12 ft16 ft

26 ft

44 ft

2804 75 $210300

A piece of sheet metal has a rectangular hole in it as shown. Find (a) the area of the piece

punched out, and (b) the area of metal left.

12 in

5.5 in

40 in

21 in

23 in

Triangles

The formulas for perimeter and area of triangles are:

• P = a + b + c

• A = ½ bh

a

b

c

h

a = h

b

c

ac

b

h

If only the sides (not the height) of a triangle are known, the area can

be found using a formula called Heron’s formula given by

where a, b and c are the sides of the triangle and s = ½ (a+b+c).

csbsassA

Find the area of the triangle below.

24 in 25 in

40 in

2283

9375.80049

5.45.195.205.44

405.44255.44245.445.44

5.44

4025242

1

in

A

s

A square hole is cut from the equilateral triangle as shown. Find the area remaining in the triangle.

10.0 cm

40 cm

2593

100693

100000,480

101020202060

cm

AAA sqtri