Transcript Points, Lines, and Planes

Areas of Parallelograms and
Triangles
Geometry
Unit 4, Lesson 1
Theorem 5-2:
Area of a Parallelogram
• The area of a parallelogram is the product
of any base and the corresponding height
• A = bh
• Any side of the parallelogram can be called
the base
Definitions
• Altitude – any
segment
perpendicular to the
line containing the
base drawn from the
side opposite the base.
Definitions
• Height – the length of
the altitude.
Find the Area
• Find the Area of the given Parallelogram:
10in
8in
12in
• A = bh = (12in)(10in) = 120in2
Example 1
• In parallelogram ABCD, DE and CF are
altitudes. Find CF to the nearest tenth.
• HINT: Find the area of
the parallelogram first
then use the area formula
to find CF.
Example 2
• A parallelogram has sides 15 cm and
18cm. The altitude perpendicular to the
containing 15 cm side is 9 cm long. Sketch
the parallelogram. Then find the length of
the altitude perpendicular to the line
containing the 18 cm side.
Theorem 5-3:
Area of a Triangle
• The area of a triangle is half the product of
any base and the corresponding height.
• A = ½bh
• You can choose any side to be the base
• The corresponding height is the length of
an altitude drawn to the line containing the
base
Find the Area:
• Find the area of the given triangle
8 cm
15 cm
• Area = ½bh = ½(15cm)(8cm) = 60cm2