# Perimeter & Area

Mrs Clark's suggested problems
Ⓟⓔⓡⓘⓜⓔⓣⓔⓡ ⓐⓝⓓ Ⓐⓡⓔⓐ
Andie D, Amanda K, Caroline F, and Melissa L

### Area of a Square

The area of a figure measures the size of the region enclosed by the figure. This is usually expressed in terms of some square unit. A few examples of the units used are square meters, square centimeters, square inches, or square kilometers.

If l is the side-length of a square, the area of the square is l2 or l × l.
Example:
What is the area of a square having side-length 3.4?
The area is the square of the side-length, which is 3.4 × 3.4 = 11.56.

### Area of a Trapezoid

If a and b are the lengths of the two parallel bases of a trapezoid, and h is its height, the area of the trapezoid is
1/2 × h × (a + b) .

Example:
What is the area of a trapezoid having bases 12 and 8 and a height of 5?
Using the formula for the area of a trapezoid, we see that the area is
1/2 × 5 × (12 + 8) = 1/2 × 5 × 20 = 1/2 × 100 = 50.

### Area of a Triangle

or
Consider a triangle with base length b and height h.
The area of the triangle is 1/2 × b × h.

Example:
What is the area of the triangle below having a base of length 5.2 and a height of 4.2?
The area of a triangle is half the product of its base and height, which is 1/2 ×5.2 × 4.2 = 2.6 × 4.2 = 10.92..

### Area of a Circle

The area of a circle is Pi × r2 or Pi × r × r, where r is the length of its radius. Pi is a number that is approximately 3.14159.
Example:
What is the area of a circle having a radius of 4.2 cm, to the nearest tenth of a square cm? Using an approximation of 3.14159 for Pi, and the fact that the area of a circle is Pi × r2, the area of this circle is Pi × 4.22 3.14159 × 4.22 =55.41…square cm, which is 55.4 square cm when rounded to the nearest tenth.

### Perimeter

The perimeter of a polygon is the sum of the lengths of all its sides.
Example:
What is the perimeter of a rectangle having side-lengths of 3.4 cm and 8.2 cm? Since a rectangle has 4 sides, and the opposite sides of a rectangle have the same length, a rectangle has 2 sides of length 3.4 cm, and 2 sides of length 8.2 cm. The sum of the lengths of all the sides of the rectangle is 3.4 + 3.4 + 8.2 + 8.2 = 23.2 cm.

# Practice Problems:

﻿(Andie's Question) 1.) Mrs. Clark wants to buy carpet for her room. Her room's measurements are below. With these measurements, How much carpeting does she need to buy to cover the entire floor?

(Caroline's Question) 2.)

Mrs. Clark wants to make a jewelry box with the square mosaic pieces below. What is the area of the box's lid?

•  jewelry-box lid

(Amanda's Question) 3.) Find the area to this triangle.

(Melissa's question) 4.)
What is the perimeter and the area to this trapezoid?

1.) 140 ft.
2.) 24 in.
3.) 32
4.) perimeter- 54 area- 112

Games:
http://www.mathplayground.com/area_perimeter.html
http://www.funbrain.com/poly/index.html
http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html

Worksheets:
http://www.superteacherworksheets.com/perimeter.html
http://www.atozteacherstuff.com/Printables/Math_Worksheets/Area___Perimeter/index.shtml

Videos:

# Emma R., Carrie H., Katherine K., Lauren L.Triangle--Emma. Circle--Carrie. Rectangle--Katherine. Lauren--Square.

﻿
Perimeter for a Triangle: add all of the sides together
Area for a Triangle: 1/2 x base x height
﻿
Practice Problem with Triangles:
1.
Find the perimeter, P, of the triangle shown below.
 Triangle

##### 2. formula being used to find the area of a triangle.
 http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i9/bk7_9i5.htm
##### Solution: problem 1
 P = 12 + 9 + 7 = 28

So, the perimeter is 28 cm.
source:
http://www.mathsteacher.com.au/year7/ch12_length/07_triangle/triangle.htm

Formulas and Practice Problems For Circles

http://www.efunda.com/math/areas/circlegen.http://www.efunda.com/math/areas/circlegen.cfm
1. Calculate the perimeter (circumference) of the circle below.

http://www.superteacherworksheets.com/perimeter.html
2. Calculate the area of the circle below:
.
http://www.mathgoodies.com/lessons/vol2/circle_area.html
1. 75.4
2. 28.3

FORMULAS AND PRACTICE PROBLEMS FOR AREA AND PERIMETER OF A RECTANGLE

AREA = Length x Width
PERIMETER = 2length + 2width
FIND THE AREA AND PERIMETER OF THE RECTANGLE

Area: 12 x 5 =60
help with perimeter and area of a rectangle
http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html
http://easycalculation.com/area/learn-rectangle.php

Square Perimeter and Area -Lauren Langdon's questions
A square is a four sided shape with equal sides. H, in the equation to the left, stands for the height of the square, and the B stands for the length of the base. So you multiply B and H to equal the area of square. Area is the amount of space in an object. Then to find the perimeter, the outside edge of a shape, of a square use the formula 4xS. That means you multiply four time S, or the length of one side. Find the area and the perimeter of each squares.

Question 1: Question 2:

Area: Area:
Perimeter: Perimeter:

1. Area- 16 inches
Perimeter- 16 inches
2. Area- 64
Perimeter- 32

Perimeter and AreaHannah T., Emma A., Kate W., Rachel T.Friday Class: Period 2

Rectangle:

Perimeter- Length is "L" and width is "W"

Perimeter Formula- P=2L+2W

Area- Length is "L" and width is "W"

Area Formula- LW

Practice Problems for Rectangles:

1) Mrs. Clark wants to buy wood to fence in her yard. Calculate the perimeter of Mrs.Clark's yard to find the amount of wood needed.
 http://www.mathsteacher.com.au/year7/ch12_length/06_rect/rect.htm

http://www.atozteacherstuff.com/Printables/Math_Worksheets/Area_Perimeter/index.shtml

2) Joe wants to redo his kitchen floor. He wants to put tile flooring in the kitchen. Use the measurements below to calculate the amount of tile flooring Joe needs in yards.

http://www.mathgoodies.com/lessons/toc_vol1.html

3) With the measurements given below find the area and perimeter of the rectangle
.

http://www.analyzemath.com/Geometry/rectangle_problems.html

4) Calculate the area and the perimeter of the following rectangle.

http://www.sparknotes.com/math/prealgebra/perimeterarea/problems.html

Answers: 1) P=160m 2) 28 square yards 3) P=22cm A= 24cm squared 4) P=18 A= 20
Useful Resources for Rectangles:
Videos- Area

Games-Perimeter and Area 1

Worksheets- Perimeter and Area 1

Square:

 http://fineartamerica.com/images-medium/swarm-of-squares-on-a-sunday-afternoon-rosemary-pierce-lackey.jpg
In the following formulas: s = side
Perimeter Formula:
P = 4s

Area Formula:
A=s²

Practice Problems for Squares:
1. Find the perimeter of a square if each side is 15m.

2. Find the area of a square courtyard if each side is 50 feet.

3. Suzie Star wants to find the perimeter of a piece of square origami paper before she makes a crane. Find the perimeter if one side is 4 inches.

4. Mrs. Clark is looking at a square coffee table for her living room. If one side of the table is 2m, what is the area of the table?

(1. 60m) (2. 2500 feet) (3. 16 inches) (4. 4 m)

Circle:

• d stands for diameter, which is the full length of the circle from one side to the next
• r stands for radius, which is half of the full length of the circle, it goes from the middle to the side
• 3.14 stands for what is Pie

Area
The formula for finding area is 3.14 x r x r

Circumference
The formulas for finding the circumference is 3.14 x d or 3.14 x r x 2

Extra Practice:

1. 1-6: Find the circumference and area of each circle using the correct formula.

#7: Mrs. McGinley needs to know how much fabric she will need for their new hot tub cover, find the area of the circle to figure out what the dimensions will be.

1) C= 9.42cm A= 28.26cm

2) C= 251.2mm A= 20,096mm

3) C= 3.14cm A= 3.14cm

4) C= 12.8dm A= 52.8dm

5) C= 16.3m A= 84.9m

6) C= 24.8cm A= 195.9cm

7) 78.5

Perimeter of a Triangle

 http://www.mathsteacher.com.au/year7/ch12_length/07_triangle/triangle.htm

### P= a+b+c

PRACTICE PROBLEMS
 http://www.tpub.com/math1/18b.htm

1) Given that a=5, b=4 and c=3, what is the perimeter?2) What is the perimeter?3) What is the perimeter?4) What is the perimeter?ANSWERS1) 122) 163) 124) 24Area of a Triangle

#### then multiplied by one half (1/2).

 Height= 4 in Base= 15 in

EXAMPLE 1:

 A
= · (15 in) · (4 in)

 A
= · (60 in2

 A
= 30 in2

Example 2:

 Height= 9 cm Base= 6 cm

 A
= · (6 cm) · (9 cm)

 A
= · (54 cm2)

 A
= 27 cm2
PRACTICE

A) If the triangle has a height of 7 cm, and a base of 6 cm, what is the area?

B) If the triangle has a height of 7 cm, and a base of 4 cm, what is the area?

A) 21 cm
B) 14 cm

Jordan A, Sara M, Serenity W, and Margie S. Period 1

Perimeter of a Square:Serenity

Circumference of a Circle:

C= 2∏ x r

R is the radius of the circle. 2R can be translated into D. D is the diameter of the circle.

Problem:

﻿

Find the circumference of the circle.

C= 2(3.14) x 14

= 6.28 x 14

= 14.96 cm

Area of a Circle:

A= ∏ x r^2 (r squared)

Problem:

Image of circle:

Find the area of the circle.

A= (3.14) x 15^2

= (3.14) x 225

= 706.5 in.

Perimeter of a Rectangle:

P = 2l + 2w

Area of a Rectangle:

A = lw

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At the park, a new brick path is being laid out. If the width of the path is 35 m and the length is 45 m, what is the perimeter of the path?

http://www.mathsteacher.com.au/year7/ch12_length/06_rect/rect.htm
What is the area of a rectangle that has a length of 9 ft. and a width of 3.5 ft.?

1.) 160 meters
2.) 31.5 squared feet

Triangle Perimeter of a triangle= side+side+side Find the perim eter of the triangle.

Answer: 9+11+10=30So the perimeter of the triangle is 30 cm. Area of a triangle= 1/2 x base/ height Find the area of the triangle. Answer: 1/2 x 6 x 3= 9So the area of the triangle is 9 cm.