18.2 polygons
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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. - PowerPoint PPT PresentationTRANSCRIPT
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