11-1 Area of Parallelograms and Triangles

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11-1 Area of Parallelograms and Triangles
You found areas of rectangles and squares.

• Find perimeters and areas of parallelograms.

• Find perimeters and areas of triangles.

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Definitions

• A quadrilateral is a polygon with four sides.

A square is a quadrilateral with four right
angles and four congruent sides.
A parallelogram is a quadrilateral with two pairs
of parallel sides.
A rectangle is a quadrilateral with four right
angles.
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What is the formula for the area of a rectangle?

• A l w

w
l
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In the Area

• Use the paper parallelogram, and label a base and
  height as shown. By cutting and rearranging
  pieces, use the area formula for a rectangle to
  help find the area formula for a parallelogram in
  terms of the length of the base and the height.

h
b
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• The area of a rectangle is the product of its
  length (l) and width (w).
• A lw

w
l
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• The are of a square is the square of its side
  length (s).
• A s 2

s
7
p. 779

• The area of a parallelogram is the product of its
  base length (b) and height (h).
• A bh

h
b
p. 779
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Perimeter RS ST UT RU 32 20 32
20 104 in.
Area Find the height of the parallelogram.
The height forms a right triangle with points S
and T with base 12 in. and hypotenuse 20
in. c2 a2 b2 Pythagorean Theorem 202 122
b2 c 20 and a 12 400 144 b2 Simplify.
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256 b2 Subtract 144 from each side. 16
b Take the positive square root of each side.
A bh Area of parallelogram (32)(16) or 512
in2 b 32 and h 16
Answer The perimeter is 104 in. and the area is
512 in2.
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A. 88 m 255 m2 B. 88 m 405 m2 C. 88 m 459
m2 D. 96 m 459 m2
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p. 781

• The area of a triangle is half the product of its
  base length (b) and corresponding height (h).
• A ½bh

h
b
p. 781
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SANDBOX You need to buy enough boards to make
the frame of the triangular sandbox shown and
enough sand to fill it. If one board is 3 feet
long and one bag of sand fills 9 square feet of
the sandbox, how many boards and bags do you need
to buy?
Step 1 Find the perimeter of the
sandbox. Perimeter 16 12 7.5 or 35.5
ft Step 2 Find the area of the sandbox.
Area of a triangle
b 12 and h 9
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Step 3 Use unit analysis to determine how many
of each item are needed.
Boards
Bags of Sand
Round the number of boards up so there is enough
wood.
Answer You will need 12 boards and 6 bags of
sand.
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Find the area of the figure.
4
49
24.6
12.3
35.26
8.2
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What is a

• quadrilateral?
• A quadrilateral is a polygon with four sides.
• parallelogram?
• A parallelogram is a quadrilateral with two pairs
  of parallel sides.
• rectangle?
• A rectangle is a quadrilateral with four right
  angles.
• square?
• A square is a quadrilateral with four right
  angles and four congruent sides.

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Area Formulas

• Rectangle A lw
• Square A s 2
• Triangle A ½bh
• Parallelogram A bh

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11-1 Assignment

• Page 10-15
• No formulas with numbers, no credit for the
  problem.