TOPIC 10-2: AREAS OF REGULAR TRIANGLES
TERM
Radius
DEFINITION
The segment connecting the center to
the corner of a polygon
The segment from the center
perpendicular to the side at its
midpoint.
Apothem
1
ARe gularPolygon  ( Perimeter )( apothem)
2
EXAMPLE 1 Find the area of the equilateral triangle.
18 m
A = _______________
EXAMPLE 2 Find the area of the regular triangle.
8 in
A = _______________
EXAMPLE 3 Find the area of a regular triangle that has a
perimeter of 24 3 cm.
A = _______________
EXAMPLE 4 A regular triangle has an apothem with a length of
2 ft. Find its area.
A = _______________
EXAMPLE 5 Find the area of a regular triangle with a radius of
10 in.
A = _______________
A#10-2, pg. 1
NAME_________________________________DATE_______________PER.______
AREAS OF REGULAR TRIANGLES
Find the area for each of the regular triangles below.
1. A = ____________
6 cm
2. A = ____________
8
3. A = ____________
6 ft
4. A = ____________
6 in
5. A = ____________
2 ft
m
A#10-2, pg. 2
6. A = ____________
Find the area of a regular triangle with a perimeter of
144 inches.
7. A = ____________
Find the area of a regular triangle with an apothem of
9 ft.
TOPIC 10-3: AREAS OF REGULAR QUADRILATERALS
1
ARe gularPolygon  ( Perimeter )( apothem)
2
EXAMPLE 1 Find the area of the square below.
9 in
A = ____________
EXAMPLE 2 Find the area of the square below.
2 2
A = ____________
EXAMPLE 3 Find the area of the square below.
5
cm
A = ____________
EXAMPLE 4 Find the area of the regular quadrilateral below.
4 in
A = ____________
EXAMPLE 5 Find the area of a square with a perimeter of 96 in.
A = ____________
A#10-3
NAME_________________________DATE_________________PER.________
AREAS OF REGULAR QUADRILATERALS
Find the areas of each of the regular quadrilaterals below.
1. A = ____________
7 in
2. A = ____________
10
m
3. A = ____________
2 cm
4. A = ____________
Find the area of a square that has a side length of 12 cm.
5. A = ____________
Find the area of a square that has an apothem length of 12 cm.
6. A = ____________
Find the area of a regular quadrilateral that has a perimeter of 88
2 m.
TOPIC 10-4: AREAS OF REGULAR HEXAGONS
ARe gularPolygon 
1
( Perimeter )( apothem)
2
EXAMPLE 1 Find the area of the regular hexagon below.
4 3 cm
A = ____________
EXAMPLE 2 Find the area of the regular polygon below.
12 cm
A = ____________
EXAMPLE 3 Find the area of the regular hexagon.
8 cm
A = ____________
EXAMPLE 4 A regular hexagon has a perimeter of 48 cm. Find its
area.
A = ____________
A#10-4
NAME__________________DATE__________________PER.______
AREAS OF REGULAR HEXAGONS
Find the area for each of the regular hexagons below.
1. A = ____________
15 m
2. A = ____________
6 ft
3. A = ____________
4 in
4. A = ____________
Find the area of a regular hexagon with a perimeter of 60 ft.
TOPIC 10-6: EFFECTS OF CHANGING DIMENSIONS ON
AREA
EXAMPLE 1 Find the area of the rectangle below.
60
8 cm
A = ____________
What would happen if we changed one or both dimensions in this
rectangle?
Original
Area
Change in
Width
Twice as
long
Change in
Length
Twice as
long
Stays the
same
Three times
as long
Four times
as long
Half
as long
One-fourth
as long
Twice as
long
New
Area
New Area
Orig. Area
What conjecture can you make regarding the changing of dimension(s)
in a two dimensional figure?
EXAMPLE 4 The area of an equilateral triangle is 36 3 square
meters. What would the new area be if its base were
doubled and height were tripled?
A = ____________
EXAMPLE 5 The area of a rhombus is 40 square inches. What
would the new area be if one diagonal was halved
and the other diagonal was doubled?
A = ____________
EXAMPLE 6 The area of a triangle is 36 square millimeters.
Suppose the height was three times as long, and the
base was four times as long. What would be the area
of the new triangle?
A = ____________
A#10-6, pg. 1
NAME___________________________DATE_________________PER.______
EFFECTS OF CHANGING DIMENSIONS ON AREA
Given an original area and the changes, find the new area of each figure.
Changes:
Width: Twice as long
Length: Three times as long
1. A = ___________
A (rectangle) = 12 cm²
2. A = ___________
A (triangle) = 27 m²
Changes:
Height: Twice as long
Base: One-third as long
3. A = ___________
A (parallelogram) = 16 in²
Changes:
Height: Three times as long
Base: One-fourth as long
4. A = ___________
A (square) = 25 yd²
Changes:
Height: Twice as long
Base: One-half as long
REVIEW
Find the area of each of the following polygons.
5. A = _____________
7 ft
5 ft
6. A = _____________
8 in
7. A = _____________
20 ft
16 ft
A#10-6, Pg. 2
8. A = _____________
6
45
10 cm
9. A = ____________
12 cm
10. A = ____________
m
cm