Transcript 11.1 Areas of Parallelograms 11.2 Areas of Triangles

Advanced Geometry
Areas and Volumes
Lesson 1
Areas
Area Formulas
** The base and the height of any polygon are
perpendicular to each other.
Parallelograms
Triangles
A  bh
1
A  bh
2
Trapezoids
1
A  h  b1  b2 
2
Rhombi
1
A  d1d 2
2
Example:
Find the area and perimeter of parallelogram
ABCD to the nearest tenth.
Example:
Find the area and perimeter of parallelogram
RSTU.
Example:
Find the length of the base of the triangle if its area is
384.25 square inches.
14.5 in.
Example:
Find the area of quadrilateral ABCD if AC = 35, BF = 18,
and DE = 10.
Example: Trapezoid WXYZ has an area of 13.75
square meters. Find WX.
Example:
Rhombus RSTU has an area of 64 square
inches. Find US if RT = 8 inches.
Areas of Regular Polygons
1
A  Pa
2
P  Perimeter
a  apothem
Example:
Find the area of a regular pentagon with a
perimeter of 90 meters to the nearest tenth.
Example:
Find the area of a regular hexagon with apothem
length of 18 inches to the nearest tenth.
Area of a Circle
A r
2
Example:
An outdoor accessories company manufactures circular
covers for outdoor umbrellas. If the cover is 8 inches
longer than the umbrella on each side, find the area of
the cover in square yards.
Example:
Find the area of the shaded region. Assume that the
quadrilateral is a square. Round to the nearest tenth.
ft
Example:
Find the area of the shaded region. Assume that the
triangle is equilateral. Round to the nearest tenth.
Example:
What is the area of the composite figure?
Round to the nearest tenth.
Example: Find the area of the composite figure.
Round to the nearest tenth, if necessary.