Transcript Area of a Regular Polygon

1. Find the area of the figure.
Round to the nearest tenth
if necessary.
2. Find the area of the figure.
Round to the nearest tenth
if necessary.
3. Find the area of the figure.
Round to the nearest tenth
if necessary.
• Find areas of regular polygons.
• Find areas of circles.
• apothem
Area of a Regular Polygon
Find the area of a regular pentagon with a perimeter
of 90 meters.
Area of a Regular Polygon
Apothem:
The central angles of a regular pentagon are
all congruent. Therefore, the measure of
each angle is
or 72.
is an apothem
of pentagon ABCDE. It bisects
a perpendicular bisector of
and is
. So,
or 36. Since the perimeter
is 90 meters, each side is 18 meters and
meters.
Area of a Regular Polygon
Write a trigonometric ratio to find the length of
.
Multiply each side by GF.
Divide each side by tan
Use a calculator.
.
Area of a Regular Polygon
Area:
Area of a regular polygon
≈ 557
Simplify.
Answer: The area of the pentagon is about 557 square
meters.
Find the area of a regular
pentagon with a perimeter of
120 inches. To the nearest
square inch.
A. 890 in2
B. 1225 in2
C. 991 in2
D. 1982 in2
A.
B.
C.
D.
A
B
C
D
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.
The diameter of the umbrella
is 72 inches, and the cover
must extend 8 inches in each
direction. So the diameter of
the cover is 8 + 72 + 8 or 88
inches. Divide by 2 to find
that the radius is 44 inches.
Area of a circle
Substitution
Use a calculator.
The area of the cover is 6082.1 square inches. To
convert to square yards, divide by 1296.
Answer: The area of the cover is 4.7 square yards to
the nearest tenth.
A swimming pool company
manufactures circular covers
for above ground pools. If the
cover is 10 inches longer than
the pool on each side, find the
area of the cover in square
yards.
2
A. 31.0 yd
B. 33.8 yd2
C. 1215.1 yd2
D. 43743.5 yd2
1.
2.
3.
4.
A
B
C
D
Area of an Inscribed Polygon
Find the area of the shaded region. Assume that the
triangle is equilateral. Round to the nearest tenth.
The area of the shaded region is
the difference between the area of
the circle and the area of the
triangle. First, find the area of the
circle.
Area of a circle
Substitution
Use a calculator.
Area of an Inscribed Polygon
To find the area of the triangle, use properties of
30-60-90 triangles. First, find the length of the
base. The hypotenuse of Δ
so RS is 3.5 and
SZ
. Since
.
Area of an Inscribed Polygon
Next, find the height of the triangle, XS.
Since m
3.5
Area of a
triangle
Use a calculator.
Answer: The area of the shaded region is 153.9 – 63.7
or 90.3 square centimeters to the
nearest tenth.