1. Perimeter distance polygon sum sides Circumference length circle cm ft
Section 1.7
Find Perimeter, Circumference, and Area
______________ is the _____________ around a ____________. It is the _______ of all the ________ of the figure. __________________ is the distance around a ________. Both are measured in units of __________, like _____ or _____. The ________ of polygons and circles is the ____________ covered by the figure. It is measured in ___________ units, like ______ or _____.
Perimeter
distance
polygon
sum
sides
Circumference
length
circle cm ft
area
surface
squared
cm²
ft²

2. Find Perimeter, Circumference, and Area
Section 1.7
Find Perimeter, Circumference, and Area
Key Concepts: Formulas for Perimeter P, Area A, and Circumference C
SQUARE
RECTANGLE
TRIANGLE
CIRCLE
length l , width w
P = 2l + 2w
A = lw
side length s
P = 4s
A = s²
side lengths a, b, c, base b, height h
P = a + b + c
A = ½bh
diameter d, radius r
C = d or C = 2r
A = r²
use 3.14 for 

3. EXAMPLE 1
Find the perimeter and area of a rectangle
Find the perimeter and area of the rectangular basketball court shown.
Perimeter
Area
2l + 2w = P A = lw
2(84) + 2(50) = =
84(50)
268 ft = =
4200 ft²

4. Find the circumference and area of a circle EXAMPLE 2
You are ordering circular cloth patches for your soccer team’s uniforms. The patch has a diameter of 8 cm. Find the approximate circumference and area of the patch shown.
Area
Circumference
r = d
A =  r ²
C = d
r = (8)
 (3.14)(4)²
 8(3.14)
 3.14(16) cm²
 cm
r = 4 cm
 cm²

5. GUIDED PRACTICE
for Examples 1 and 2
Find the area and perimeter (or circumference) of the figure. If necessary, round to the nearest tenth. 2.
P = 2l + 2w
= 2(13) + 2(6) =
= 38 m
A = l  w
= 13(6)
= 78 m²
 2(2)(3.14)
 12.56
C = 2r
 12.6 yd
 (3.14)(2)²
 12.56
 12.6 yd²
A =  r ²

6. Standardized Test Practice
EXAMPLE 3
Standardized Test Practice
Find side lengths QR and RS (Distance Formula) ans QS ( use | x1 – x2| )
QS =
1 – 5 =
| –4 | = 4 5
4.1
QR =
RS = 4
Perimeter is: P = =
13.1 units

7. Solve a multi-step problem
EXAMPLE 4
Solve a multi-step problem
60 ft
You need to mow the lawn in your
backyard. You also need to use the
trimmer around the edge. The
rectangular lawn is 30 feet by 60 feet.
It takes 3 minutes to mow 200 square feet and 2 minutes to edge 30 feet. How many minutes will it take to do both jobs?
30 ft
Area
Perimeter of lawn.
A = lw
= 60(30)
= 1800 ft²
P = 2l + 2w
= 2(60) + 2(30)
= 180 ft
Time to mow
Time to trim
1800 ÷ 200 = 9
12 min
9(3 min.) =
27 min
180 ÷30 = 6
6(2 min. ) = =
39 minutes

8. GUIDED PRACTICE
for Examples 3 and 4
3. Describe how to find the height from F to EG in the triangle.
The height is the segment from point F to EG at the point (1,3).
The height length is 6.

9. GUIDED PRACTICE
for Examples 3 and 4
Find the perimeter and the area of the triangle shown. 4. EF =
(1 – 7) + (6 – 3) 2 = 45
6.7 GF =
(1 – 7) + (2 – 3) 2 = 37
6.1 EG =
2 – 6
| –4 | = 4 1 2 A = bh
P = EF + GF + EG =
= 16.8 un = 1 2
(4) 6 =
12 un²

10. EXAMPLE 5 Find unknown length
The base of a triangle is 28 meters. Its area is 308 square meters. Find the height of the triangle. 1 2 A = bh
Area formula =
308 1 2
(28) h
Substitute 308 for A and 28 for b. =
308
14h
Half of 28. = 22 h
Divide by 14.
h = 22 m

11. GUIDED PRACTICE
for Example 5
5. The area of a triangle is 64 square meters, and its height is 16 meters. Find the length of its base. 1 2 A = bh = 64 1 2
(16) b = 64 8b = 8 b
b = 8 m