Area of a Parallelogram, Triangle, and Trapezoid

1
Area of a Parallelogram, Triangle, and Trapezoid

• 11.4 AND 11.5

2
Objective

• You will be able to find the areas of
  parallelograms, triangles, and trapezoids.
• Word Watch
• -base of a parallelogram
• -height of a parallelogram
• -base of a triangle
• -height of a triangle
• -bases of a trapezoid
• -height of a trapezoid

3

• The base of a parallelogram is the length of any
  one of the sides.
• The height of a parallelogram is the
  perpendicular distance between the side whose
  length is the base and the opposite sides.

height
base
4
Area of a Parallelogram

• The area A of a parallelogram is the product of a
  base and the corresponding height.
• A bh

base b
height h
5
Example Find the Area of a Parallelogram

• Find the area of the parallelogram.
• A bh write the formula for area
• 10(6) substitute 10 for b
• and 6 for h
• 60 multiply
• Answer The area of the parallelogram is 60
  square centimeters or 60 cm

6 cm
10 cm
2
6
? YOUR TURN! ?

• Find the area of the parallelogram with the given
  base and height.
• 1) b 8 in, h 11 in
• 2) b 9.3 m, h 7 m

88 in
2
65.1 m
2
7

• The base of a triangle is the length of any one
  of the sides.
• The height of a triangle is the perpendicular
  distance between the side whose length is the
  base and the vertex opposite that side.

height h
base b
8
Area of a Triangle

• The area A of a triangle is half the product of a
  base and the corresponding height.
• A bh

1 2
9
Find the Area of a Triangle
1 2

• A bh
• (231)(111)
• 12,820.5
• ANSWER The area of the triangle is 12,820.5
  square feet.

Write formula for area of a triangle
111 ft
1 2
231 ft
Substitute 231 for b and 111 for h.
Multiply
10
? YOUR TURN! ?

• Find the area of the triangle with a base of 9 ft
  and a height of 6 ft.

1 2
A (9)(6)
6 ft
1 2
A 54
9 ft
2
A 27 ft
11
TRAPEZOIDS

• You can use the bases and the height of a
  trapezoid to find the area of the trapezoid.
• The lengths of the parallel sides of a trapezoid
  are the bases of a trapezoid.
• The height of a trapezoid is the perpendicular
  distance between the bases.

base b
1
height h
base b
2
12
Area of a Trapezoid

• The area A of a trapezoid is half the product of
  the sum of the bases and the height.
• A (b b )h

1 2
1
2
13
Find the Area of a Trapezoid
5 ft
1 2

• A (b b )h
• A (5 10)8
• A (15)8
• A (120)

2
1
8 ft
1 2
10 ft
1 2
The area of the trapezoid is 60 square feet.
1 2
A 60
14
? YOUR TURN! ?

• Find the area of the trapezoid with the given
  bases and height.
• b 13 in, b 15 in, h 6 in

2
1
84 in
2
15
THOUGHT OF THE DAY!

• The sentence
• "The quick brown fox jumps over the lazy dog"
• uses every letter of the alphabet.