This document provides instruction on using formulas in geometry, including formulas for perimeter, area, circumference, midpoint, distance, and more. It includes examples of applying these formulas to find measurements of shapes on a coordinate plane. Key formulas and concepts covered include perimeter, area, circumference of circles, midpoint formula, distance formula, and Pythagorean theorem. Practice problems are provided for students to demonstrate their understanding.

1. 1-5 Using Formulas in Geometry
Drill #5 9/11/14
Evaluate. Round to the nearest hundredth.
1. 122
2. 7.62
3.
4.
5. 32()
6. (3)2
144
57.76
8
7.35
28.27
88.83
Holt McDougal Geometry

2. 1-5 Using Formulas in Geometry
Apply formulas for perimeter, area, and
circumference.
Holt McDougal Geometry
Objective

3. 1-5 Using Formulas in Geometry
Develop and apply the formula for midpoint.
Use the Distance Formula and the
Pythagorean Theorem to find the distance
between two points.
Holt McDougal Geometry
Objectives

4. 1-5 Using Formulas in Geometry
perimeter diameter
area radius
base circumference
height pi
Holt McDougal Geometry
Vocabulary

5. 1-5 Using Formulas in Geometry
• Make a list of any math formula you know
and be able to explain how to use it.
Holt McDougal Geometry

6. 1-5 Using Formulas in Geometry
1. Graph A (–2, 3) and B (1, 0).
2. Find CD. 8
3. Find the coordinate of the midpoint of CD. –2
4. Simplify.
4
Holt McDougal Geometry

8. 1-5 Using Formulas in Geometry
The perimeter P of a plane figure is
the sum of the side lengths of the
figure.
The area A of a plane figure is the
number of non-overlapping square
units of a given size that exactly
cover the figure.
Holt McDougal Geometry

9. 1-5 Using Formulas in Geometry
Holt McDougal Geometry

10. 1-5 Using Formulas in Geometry
The base b can be any side of a
triangle. The height h is a segment
from a vertex that forms a right angle
with a line containing the base. The
height may be a side of the triangle or
in the interior or the exterior of the
triangle.
Holt McDougal Geometry

11. 1-5 Using Formulas in Geometry
Remember!
Perimeter is expressed in linear
units, such as inches (in.) or meters
(m). Area is expressed in square
units, such as square centimeters
(cm2).
Holt McDougal Geometry

12. 1-5 Using Formulas in Geometry
Example 1A: Finding Perimeter and Area
Find the perimeter and area of each figure.
Holt McDougal Geometry
= 2(6) + 2(4)
= 12 + 8 = 20 in.
= (6)(4) = 24 in2

13. 1-5 Using Formulas in Geometry
Example 1B: Finding Perimeter and Area
Find the perimeter and area of each figure.
P = a + b + c
= (x + 4) + 6 + 5x
= 6x + 10
Holt McDougal Geometry
= 3x + 12

14. 1-5 Using Formulas in Geometry
Check It Out! Example 1
Find the perimeter and area of a square with
s = 3.5 in.
P = 4s
Holt McDougal Geometry
A = s2
P = 4(3.5) A = (3.5)2
P = 14 in. A = 12.25 in2

15. 1-5 Using Formulas in Geometry
Example 2: Crafts Application
The Queens Quilt block includes 12 blue
triangles. The base and height of each triangle
are about 4 in. Find the approximate amount of
fabric used to make the 12 triangles.
The area of one triangle is
The total area of the 12 triangles is
12(8) = 96 in2.
Holt McDougal Geometry

16. 1-5 Using Formulas in Geometry
Holt McDougal Geometry
Check It Out! Example 2
Find the amount of fabric used to make four
rectangles. Each rectangle has a length of in.
and a width of in.
The area of one triangle is
The amount of fabric to make four rectangles is

17. 1-5 Using Formulas in Geometry
In a circle a diameter is a segment that
passes through the center of the circle and
whose endpoints are on a circle. A radius of
a circle is a segment whose endpoints are the
center of the circle and a point on the circle.
The circumference of a circle is the distance
around the circle.
Holt McDougal Geometry

18. 1-5 Using Formulas in Geometry
The ratio of a circle’s circumference to its
diameter is the same for all circles. This ratio
is represented by the Greek letter  (pi). The
value of  is irrational. Pi is often
approximated as 3.14 or .
Holt McDougal Geometry

19. 1-5 Using Formulas in Geometry
Example 3: Finding the Circumference and
Holt McDougal Geometry
Area of a Circle
Find the circumference and area of a circle with
radius 8 cm. Use the  key on your calculator.
Then round the answer to the nearest tenth.
 50.3 cm  201.1 cm2

20. 1-5 Using Formulas in Geometry
Check It Out! Example 3
Find the circumference and area of a circle
with radius 14m.
 88.0 m  615.8 m2
Holt McDougal Geometry

21. 1-5 Using Formulas in Geometry
Holt McDougal Geometry
Lesson Quiz: Part I
Find the area and perimeter of each figure.
1. 2.
3.
23.04 cm2;
19.2 cm
x2 + 4x; 4x + 8
10x; 4x + 16

22. 1-5 Using Formulas in Geometry
Holt McDougal Geometry
Lesson Quiz: Part II
Find the circumference and area of each circle.
Leave answers in terms of .
4. radius 2 cm
4² cm; 4 cm2
5. diameter 12 ft
36 ft 2; 12 ft
6. The area of a rectangle is 74.82 in2, and the
length is 12.9 in. Find the width.
5.8 in

23. 1-5 Using Formulas in Geometry
A coordinate plane is a plane that is
divided into four regions by a horizontal
line (x-axis) and a vertical line (y-axis) .
The location, or coordinates, of a point are
given by an ordered pair (x, y).
Holt McDougal Geometry

24. 1-5 Using Formulas in Geometry
Holt McDougal Geometry

25. 1-5 Using Formulas in Geometry
Helpful Hint
To make it easier to picture the problem, plot
the segment’s endpoints on a coordinate
plane.
Holt McDougal Geometry

26. 1-5 Using Formulas in Geometry
Example 1: Finding the Coordinates of a Midpoint
Find the coordinates of the midpoint of PQ
with endpoints P(–8, 3) and Q(–2, 7).
Holt McDougal Geometry
= (–5, 5)

27. 1-5 Using Formulas in Geometry
Check It Out! Example 1
Find the coordinates of the midpoint of EF
with endpoints E(–2, 3) and F(5, –3).
Holt McDougal Geometry

28. 1-5 Using Formulas in Geometry
Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates
(2, 7) and M has coordinates (6, 1). Find
the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:
Holt McDougal Geometry

29. 1-5 Using Formulas in Geometry
Holt McDougal Geometry
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates equal.
Multiply both sides by 2.
12 = 2 + x Simplify.
– 2 –2
10 = x
Subtract.
Simplify.
2 = 7 + y
– 7 –7
–5 = y
The coordinates of Y are (10, –5).

30. 1-5 Using Formulas in Geometry
Check It Out! Example 2
S is the midpoint of RT. R has coordinates
(–6, –1), and S has coordinates (–1, 1). Find
the coordinates of T.
Step 1 Let the coordinates of T equal (x, y).
Step 2 Use the Midpoint Formula:
Holt McDougal Geometry

31. 1-5 Using Formulas in Geometry
Check It Out! Example 2 Continued
Step 3 Find the x-coordinate.
Holt McDougal Geometry
Set the coordinates equal.
Multiply both sides by 2.
–2 = –6 + x Simplify.
+ 6 +6
4 = x
Add.
Simplify.
2 = –1 + y
+ 1 + 1
3 = y
The coordinates of T are (4, 3).

32. 1-5 Using Formulas in Geometry
The Ruler Postulate can be used to find the distance
between two points on a number line. The Distance
Formula is used to calculate the distance between
two points in a coordinate plane.
Holt McDougal Geometry

33. 1-5 Using Formulas in Geometry
Example 3: Using the Distance Formula
Find FG and JK.
Then determine whether FG  JK.
Step 1 Find the
coordinates of each point.
F(1, 2), G(5, 5), J(–4, 0),
K(–1, –3)
Holt McDougal Geometry

34. 1-5 Using Formulas in Geometry
Holt McDougal Geometry
Example 3 Continued
Step 2 Use the Distance Formula.

35. 1-5 Using Formulas in Geometry
Check It Out! Example 3
Find EF and GH. Then determine if EF  GH.
Step 1 Find the coordinates of
each point.
E(–2, 1), F(–5, 5), G(–1, –2),
H(3, 1)
Holt McDougal Geometry

36. 1-5 Using Formulas in Geometry
Check It Out! Example 3 Continued
Step 2 Use the Distance Formula.
Holt McDougal Geometry

37. 1-5 Using Formulas in Geometry
You can also use the Pythagorean Theorem to
find the distance between two points in a
coordinate plane. You will learn more about the
Pythagorean Theorem in Chapter 5.
In a right triangle, the two sides that form the
right angle are the legs. The side across from the
right angle that stretches from one leg to the
other is the hypotenuse. In the diagram, a and b
are the lengths of the shorter sides, or legs, of the
right triangle. The longest side is called the
hypotenuse and has length c.
Holt McDougal Geometry

38. 1-5 Using Formulas in Geometry
Holt McDougal Geometry

39. 1-5 Using Formulas in Geometry
Example 4: Finding Distances in the Coordinate Plane
Use the Distance Formula and the
Pythagorean Theorem to find the distance, to
the nearest tenth, from D(3, 4) to E(–2, –5).
Holt McDougal Geometry

40. 1-5 Using Formulas in Geometry
Holt McDougal Geometry
Example 4 Continued
Method 1
Use the Distance Formula. Substitute the
values for the coordinates of D and E into the
Distance Formula.

41. 1-5 Using Formulas in Geometry
Method 2
Use the Pythagorean Theorem. Count the units for
sides a and b.
Holt McDougal Geometry
Example 4 Continued
a = 5 and b = 9.
c2 = a2 + b2
= 52 + 92
= 25 + 81
= 106
c = 10.3

42. 1-5 Using Formulas in Geometry
Check It Out! Example 4a
Use the Distance Formula and the
Pythagorean Theorem to find the distance,
to the nearest tenth, from R to S.
R(3, 2) and S(–3, –1)
Method 1
Use the Distance Formula. Substitute the
values for the coordinates of R and S into the
Distance Formula.
Holt McDougal Geometry

43. 1-5 Using Formulas in Geometry
Check It Out! Example 4a Continued
Use the Distance Formula and the
Pythagorean Theorem to find the distance,
to the nearest tenth, from R to S.
R(3, 2) and S(–3, –1)
Holt McDougal Geometry

44. 1-5 Using Formulas in Geometry
Check It Out! Example 4a Continued
Method 2
Use the Pythagorean Theorem. Count the units for
sides a and b.
a = 6 and b = 3.
c2 = a2 + b2
= 62 + 32
= 36 + 9
= 45
Holt McDougal Geometry

45. 1-5 Using Formulas in Geometry
Check It Out! Example 4b
Use the Distance Formula and the
Pythagorean Theorem to find the distance,
to the nearest tenth, from R to S.
R(–4, 5) and S(2, –1)
Method 1
Use the Distance Formula. Substitute the
values for the coordinates of R and S into the
Distance Formula.
Holt McDougal Geometry

46. 1-5 Using Formulas in Geometry
Check It Out! Example 4b Continued
Use the Distance Formula and the
Pythagorean Theorem to find the distance,
to the nearest tenth, from R to S.
R(–4, 5) and S(2, –1)
Holt McDougal Geometry

47. 1-5 Using Formulas in Geometry
Check It Out! Example 4b Continued
Method 2
Use the Pythagorean Theorem. Count the units for
sides a and b.
a = 6 and b = 6.
c2 = a2 + b2
= 62 + 62
= 36 + 36
= 72
Holt McDougal Geometry

48. 1-5 Using Formulas in Geometry
Example 5: Sports Application
A player throws the ball
from first base to a point
located between third
base and home plate and
10 feet from third base.
What is the distance of
the throw, to the nearest
tenth?
Holt McDougal Geometry

49. 1-5 Using Formulas in Geometry
Set up the field on a coordinate plane so that home
plate H is at the origin, first base F has coordinates
(90, 0), second base S has coordinates (90, 90), and
third base T has coordinates (0, 90).
The target point P of the throw has coordinates (0, 80).
The distance of the throw is FP.
Holt McDougal Geometry
Example 5 Continued

50. 1-5 Using Formulas in Geometry
Check It Out! Example 5
The center of the pitching
mound has coordinates
(42.8, 42.8). When a
pitcher throws the ball from
the center of the mound to
home plate, what is the
distance of the throw, to
the nearest tenth?
 60.5 ft
Holt McDougal Geometry

51. 1-5 Using Formulas in Geometry
1. Find the coordinates of the midpoint of MN with
endpoints M(-2, 6) and N(8, 0).
2. K is the midpoint of HL. H has coordinates (1, –7),
and K has coordinates (9, 3). Find the coordinates
of L.
3. Find the distance, to the nearest tenth, between
Holt McDougal Geometry
Lesson Quiz: Part I
(17, 13)
(3, 3)
12.7
S(6, 5) and T(–3, –4).
4. The coordinates of the vertices of ΔABC are A(2, 5),
B(6, –1), and C(–4, –2). Find the perimeter of
ΔABC, to the nearest tenth. 26.5

52. 1-5 Using Formulas in Geometry
Holt McDougal Geometry
Lesson Quiz: Part II
5. Find the lengths of AB and CD and determine
whether they are congruent.