1. Perimeter, Lines, & Angles
GHSGT Review
Perimeter, Lines, & Angles

2. Perimeter Perimeter is defined as the distance around a figure
You can find perimeter for a polygon by adding its side lengths
The perimeter of a circle is called its circumference, using the formula C = πd, where d is the length of the diameter

3. Quadrilaterals
Here are the 4-sided figures you need to be familiar with:
Rectangle Square
Parallelogram Trapezoid

4. Polygons
These are some important polygons; memorize the number of sides each one has:
Triangle – 3 sides Pentagon – 5 sides
Hexagon – 6 sides Octagon – 8 sides

5. Regular Polygons
A polygon is “regular” if it has equal side lengths and equal angle measures.
A regular triangle would have each angle measuring 60o, because 180 ÷ 3 = 60
60o
7 cm
7 cm
60o
60o
7 cm

6. Example Find the perimeter of the pentagon shown:
The perimeter is the sum of its side lengths
P = = (3)(5 sides) = 15 in.
3 in
3 in
3 in
3 in
3 in

7. Example
Q: A regular hexagon has a perimeter of 72 feet. What is the length of each of its sides?
A: Regular means that all sides are equal, so 72 ÷ 6 congruent sides = 12 feet each

8. Circumference
You saw before that C = πd to find the perimeter of a circle
This circle has a radius of 3 cm
To find its circumference,
Double the radius to get that its diameter is 6cm, then C = (3.14)(6) = cm
3 cm

9. 1. The perimeters of the two triangles are equal
1. The perimeters of the two triangles are equal. What is the value of x?
A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm
6 cm x
10 cm
8 cm
10 cm
8 cm

10. 2. A hexagon has a perimeter of 25
2. A hexagon has a perimeter of 25. Five of its sides are 3, 3, 4, 6, and 6. What is the length of the remaining side?
A. 2
B. 3
C. 4
D. 5

11. 3. The regular hexagon shown here has the same perimeter as a square with a side of 18 inches. How long is each side of the hexagon?
A. 10 inches
B. 12 inches
C. 24 inches
D. 72 inches

12. 4. Jeffrey has an irregularly shaped backyard, as shown
4. Jeffrey has an irregularly shaped backyard, as shown. What is the perimeter of his backyard?
A. 170 feet
B. 180 feet
C. 200 feet
D. 300 feet
40 ft
60 ft
60 ft
40 ft
100 ft

13. 5. The circumference of the circle below is 31. 4 inches
5. The circumference of the circle below is 31.4 inches. Find its diameter.
A. 3.2 inches
B. 5 inches
C. 10 inches
D inches
C = 31.4 inches

14. Solutions
1. D – The perimeter of the first triangle is 26. To get x, subtract the sum of the two sides of the second triangle from this number.
2. B – Add the five sides of the hexagon, and then subtract this number from the perimeter of 25 that was given.
3. B – The perimeter of the square is (18)(4 sides) = 72. Then divide 72 by 6 sides to get the side length of the hexagon.

15. Solutions, continued
4. D – Add up all of the sides to get that his backyard has perimeter 300 feet.
5. C – Use the formula C = πd to substitute:
31.4 = (3.14)(d)
Then divide the 3.14 from both sides to find that d = 10 inches.