Ch 10.5
Find the area of the figure. Round
to the nearest tenth if necessary.
5 (10 + 18) = 70
2
Trapezoid LMNO has an area of 55
square units. Find the height.
55 = h (8 + 14)  h = 5
2
Find the height of a trapezoid that has an area of 64
square inches, and bases of 8 and 12 inches.
64 = h (8 + 12)
2
 h = 6.4 cm
Ch 10.5
Ch 10.5
Areas of Regular Polygons
Learning Target:
I will be able to find the areas of regular polygons.
Standard 10.0
Students compute areas of polygons.
Ch 10.5
Area of a Regular Polygon
FURNITURE The top of the table
shown is a regular hexagon with
a side length of 3 feet and an
apothem of 1.7 feet. What is the
area of the tabletop to the
nearest tenth?
Step 1 Since the polygon has 6 sides, the polygon
can be divided into 6 congruent isosceles
triangles, each with a base of 3 ft and a
height of 1.7 ft.
Ch 10.5
Area of a Regular Polygon
Step 2
Find the area of one triangle.
Area of a triangle
b = 3 and h = 1.7
= 2.55 ft2
Simplify.
Step 3 Multiply the area of one triangle by the total
number of triangles.
Since there are 6 triangles, the area of the table is
2.55 ● 6 or 15.3 ft2.
Ch 10.5
UMBRELLA The top of an
umbrella shown is a regular
hexagon with a side length of
2 feet and an apothem of
1.5 feet. What is the area of
the entire umbrella to the
nearest tenth?
A. 6 ft2
B. 7 ft2
C. 8 ft2
D. 9 ft2
Ch 10.5
center of a regular polygon
a point in the interior that is equidistant from all
the vertices.
apothem
a segment drawn from the center that is
perpendicular to a side of the regular
polygon.
Note: In any regular polygon, all apothems are
congruent.
Ch 10.5
Identify Center and Apothem in Regular Polygons
In the figure, pentagon PQRST is inscribed in
Identify the center and apothem of the polygon.
center: point X
apothem: XN
Ch 10.5
Theorem 10-5
Ch 10.5
Use the Formula for the Area of a Regular
Polygon
A. Find the area of the
regular hexagon with a
side length of 5 meters
and an apothem of
2.5√3 meters.
2.5√3 m
Area of a regular polygon
≈ 65.0 m2
Use a calculator.
Ch 10.5
A. Find the area of the regular hexagon with sides
of 7.5 m and apothem of 6.5 m. Round to the
nearest tenth.
A. 73.1 m2
B. 96.5 m2
C. 126.8 m2
D. 146.3 m2
Ch 10.5

Use the Formula for the Area of a Regular
Polygon
B. Find the area of the
regular pentagon with a
side length of 10.58 cm
and an apothem of
7.28 cm. Round to the
nearest tenth.
Area of a regular polygon

1
2
7.28 5 10 .58 
Use a calculator.
Ch 10.5
B. Find the area of the regular pentagon with a side
length of 7 m and an apothem of 6.5 m. Round to
the nearest tenth.
A. 113.8 m2
B. 124.5 m2
C. 138.9 m2
D. 143.1 m2
Ch 10.5
Find the Area of a Composite Figure by
Subtracting
Find the area of the shaded figure.
To find the area of the figure, subtract the area of the
smaller rectangle from the area of the larger rectangle.
The length of the larger rectangle is 25 + 100 + 25 or
150 feet. The width of the larger rectangle is 25 + 20 +
25 or 70 feet.
Ch 10.5
Find the Area of a Composite Figure by
Subtracting
area of shaded figure = area of larger rectangle
– area of smaller rectangle
Area formulas
Substitution
Simplify.
Simplify.
Ch 10.5
INTERIOR DESIGN Cara wants to wallpaper one wall
of her family room. She has a fireplace in the center
of the wall. Find the area of the wall around the
fireplace.
A. 168 ft2
B. 156 ft2
C. 204 ft2
D. 180 ft2