12'2 Quadrilaterals

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12.2 Quadrilaterals
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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
h
Base and height always form right angles
b
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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)

h
b
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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

b
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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

b
h
b
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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
d
c
h
b
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The area of a rectangle is 280 sq cm. Its width
is 14 cm. Find its length.
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A respirator unit needs a rectangular floor space
of 0.79 m by 1.2 m. How many units could be
placed in a storeroom having 20 sq m of floor
space?
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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?
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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.
40 in
12 in
23 in
5.5 in
21 in
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12.3 Triangles
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A right triangle is a triangle that has a right
(90 degree) angle. The 2 sides that form the
right angle are called the legs of the triangle
and the side opposite the right angle is called
the hypotenuse.
leg
hypotenuse
leg
leg
hypotenuse
leg
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The Pythagorean Theorem relates the sides of any
right triangle. If a and b represent the legs and
c the hypotenuse, then
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Find the length of the hypotenuse
c
24 dm
10 dm
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Find the length of the hypotenuse
8.00 cm
3.90 cm
c
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Find the length of the missing side
25.0 m
18.0 m
b
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Find the length of the missing side
42,600 ft
37,800 ft
b
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• How long must a guy wire be to reach from the top
  of a 15-m telephone pole to a point on the ground
  10 m from the foot of the pole?
• Use the Pythagorean theorem.

c
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The formulas for perimeter and area of triangles
are

• P a b c
• A ½ bh

c
a h
b
c
a
c
h
h
a
b
b
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If only the sides (not the height) of a triangle
are known, the area can be found using a formula
called Herons formula given bywhere a, b and
c are the sides of the triangle and s ½
(abc).
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Find the area of the triangle below.
24 in
25 in
40 in
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A square hole is cut from the equilateral
triangle as shown. Find the area remaining in the
triangle.
10.0 cm
40 cm