Unit 2 Parent Guide: Area of Polygons
Unit 2 Key
b = base
h = height (perpendicular to base
b₁ = base 1 of a trapezoid
b₂ = base 2 of a trapezoid
Vocabulary
 Perimeter (P): The distance around a figure (add all sides).
 Area (A): The amount of surface covered or enclosed by a figure.
 Trapezoid: A quadrilateral with exactly one pair of parallel sides.
 Complex Figure: A figure made by combining simple geometric figures.
2-1: Perimeter and Area of Rectangles
A = lw or A = bh
w
P = add all sides
P=2+6+2+6
P = 16 in
h
l
Example 1: Find the perimeter and area of the rectangle.
A = bh
A=6∙2
A = 12 in²
)
b
2 in
6 in
Example 2: Find the missing value on the rectangle.
Step 1: Place the values you know into the area formula (A = bh).
Step 2: Solve for the missing value (divide both sides by 2).
Step 3: Label your answer.
2-2: Perimeter and Area of Right Triangles
12 = b ∙ 2
2
2
6 in = b
A = ½ bh or A =
b
𝒃𝒉
𝟐
h
Example 1: Find the perimeter and area of the triangle.
P = add all sides
P = 8 + 4 + 10
P = 22 ft
A=
A=
A=
b
𝒃𝒉
𝟐
10 ft
𝟒 ∙𝟖
8 ft
𝟐
𝟑𝟐
𝟐
A = 12 in²
= 16 ft²
4 ft
Example 2: Find the missing value on the triangle.
Step 1: Place the values you do know into the area formula (A =
𝒃𝒉
𝟐
).
16 =
𝟒∙𝒉
𝟐
𝟒∙𝒉
Step 2: Solve for the missing value (multiply both sides by 2).
2 ∙ 16 = 𝟐 ∙ 2
Step 3: Continue solving for the missing value (divide both sides by 4). 32 = 4 ∙ h
4
4
Step 4: Label your answer.
8 ft = h
h
A = 16 ft²
4 ft
2-3: Perimeter and Area of Parallelograms
h
A = bh
b
Example: Find the perimeter and area of the parallelogram.
P = add all sides
P=5+7+5+7
P = 24 cm
A = bh
A=7∙3
A = 21 cm²
5 cm
3 cm
7 cm
2 in
2-4: Perimeter and Area of Any Triangle
A = ½ bh or A =
𝒃𝒉
𝟐
Example: Find the perimeter and area of the triangle.
P = add all sides
P = 4 + 6 + 10
A=
A=
P = 20 in
A=
𝒃𝒉
𝟐
𝟔 ∙𝟑
𝟐
𝟏𝟖
𝟐
10 in
3 in
4 in
= 9 in²
6 in
2-5: Reviews Previous Lessons
b₁
2-6: Perimeter and Area of Trapezoids
A = ½ h(b₁ + b₂) or A = (
𝒃₁+ 𝒃₂
𝟐
)h
h
b₂
Example: Find the perimeter and area of the trapezoid.
P = add all sides
P = 4 + 11 + 4 + 7
𝑏₁+ 𝑏₂
A=(
2
7+ 11
A=(
P = 26 in
2
7 in
)h
)∙3
3 in
4 in
18
A=(2)∙3
11 in
A = 9 ∙ 3 = 27 in²
2-7: Perimeter and Area of Complex Figures
Hint: Divide the figure into simple shapes (rectangles, squares, triangles, etc.).
Example 1: Find perimeter (find missing measurements and add all sides together).
7 cm
3 cm
1 cm
y
5 cm
x
7 cm
Use the given measurements to find the unknown measurements.
5–1=4
7–3=4
x = 4 cm
y = 4 cm
5 cm Add all sides together to find perimeter.
P=5+7+4+4+1+3
P = 24 cm
Example 2: Find area (find the area of each simple shape and add them together).
Shape W: A = bh
Shape Z: A = bh
3 cm
A
=
3
∙
5
A = 4 ∙4
1 cm
A = 15 cm²
A = 16 cm ²
4 cm
Add the areas of the simple shapes together.
5 cm
W
W + Z = 15 + 16 = 31 cm²
Z
4 cm
7 cm
2-7 Continued
Example 3: Find the area of the shaded part of the figure.
Step 1: Find the area of the entire triangle.
𝑏ℎ
A= 2
A=
Step 2: Find the area of the empty space.
𝑏ℎ
A= 2
6 ∙8
A=
A=
2
48
2
= 24 cm²
A=
6 ∙3
2
18
2
= 9 cm²
Step 3: Subtract the empty space from the entire triangle (entire area – empty space = shaded area).
24 cm² - 9 cm² = 15 cm²
2-8: Perimeter and Area of Regular Polygons
Pentagon: 5-sided polygon
Hexagon: 6-sided polygon
Octagon: 8-sided polygon
P = add all sides
P=6+6+6+6+6
A = find the area of one triangle and multiply by the number of sides
𝑏ℎ
A= 2
P = 30 ft
A=
A=
6 ∙5
2
30
= 15 ft² (area of 1 triangle)
x 5 (5 sides)
A = 75 ft²
2
5 ft
6 ft
2-9: Polygons on the Coordinate Plane
A. Plot these points on the coordinate plane: A(2,2) B(2, 10). Plot point C to make a right triangle
with base AC measuring 6 units long. What ordered pair locates point C? C(8,2)
B. Draw line segments to form triangle ABC. Segment BC measures 10 units. Find the perimeter and
area of triangle ABC.
a. To find the
i. Count
plane, or
length of the missing sides:
the units on the coordinate
ii. Use the ordered pairs (x,y). If the x-values are the same, subtract the y-values. If
the y-values are the same, subtract the x-values.
AB:
A(2,2)
B(2,10)
x-values are the same
subtract the y-values (10 – 2 = 8 units)
AC:
A(2,2)
C(8,2)
y-values are the same
subtract the y-values (8 – 2 = 6 units)
b. Now find the perimeter and area of the triangle.
𝑏ℎ
P = add all sides
A= 2
P = 8 + 6 + 10 = 24 units
A=
6 ∙8
2
=
48
2
= 24 units²
Remember to keep this study guide all year to help with studying for assessments and
end of year tests. 