11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.
-
Upload
natalie-henderson -
Category
Documents
-
view
218 -
download
0
Transcript of 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.
![Page 1: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/1.jpg)
11.1 – Areas of Triangles and Parallelograms
![Page 2: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/2.jpg)
Square:
A = s2
![Page 3: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/3.jpg)
Rectangle:
A = bh
![Page 4: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/4.jpg)
Parallelogram:
A = bh
Note: The height is the perpendicular distance between the parallel sides
![Page 5: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/5.jpg)
Triangle:
![Page 6: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/6.jpg)
A bh1
2
Note: The height is the perpendicular line
Triangle:
![Page 7: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/7.jpg)
If two polygons are _______________, then they have the same ____________.
congruentareas
![Page 8: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/8.jpg)
Find the area of the shape.
A = s2
A = (11)2
A = 121 u2
![Page 9: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/9.jpg)
Find the area of the shape.
A = bh
A = (9)(3)
A = 27 u2
![Page 10: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/10.jpg)
Find the area of the shape.
A = bh
A = (16)(10)
A = 160 u2
12
![Page 11: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/11.jpg)
Find the area of the shape.
A bh1
2
A1
(8)(16)2
A 4(16)
A u264
24
![Page 12: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/12.jpg)
Find the area of the shape.
A = bh
A = (12)(8)
A = 96 u2
10
![Page 13: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/13.jpg)
The lengths of the hypotenuse and one leg of a right triangle are given. Find the perimeter and area of the triangle.
Hypotenuse: 17ft; leg: 8ft
17ft
8ft
c2 = a2 + b2
172 = a2 + 82
289 = a2 + 64225 = a2
15 = a
15ft
P = 8 + 15 + 17P = 40ft
A bh1
2
A1
(8)(15)2
A 4(15) 60ft2
![Page 14: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/14.jpg)
The lengths of the hypotenuse and one leg of a right triangle are given. Find the perimeter and area of the triangle.
Hypotenuse: 53in; leg: 45in
53in
45in
c2 = a2 + b2
532 = a2 + 452
2809 = a2 + 2025784 = a2
28 = a
28in
P = 28 + 45 + 53P = 126in
A bh1
2
A1
(45)(28)2
A = 630in2
![Page 15: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/15.jpg)
Find the value of x.
A = bh
576 = x 18
32in = x
![Page 16: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/16.jpg)
Find the value of x.
A bh1
2
x1
70 (10)2
x70 5
cm x14
![Page 17: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/17.jpg)
Find the value of x.
A = bh
104 = 16x
6.5in = x
![Page 18: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/18.jpg)
The area of a region is the _______ of the areas of its nonoverlapping parts.
sum
![Page 19: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/19.jpg)
Find the area of the shaded figure.
A = +3
10 10
6
A = bh1
2+ bh
A = 1
(10)(3)2
+ (10)(6)
A = + 6015
A = 75m2
![Page 20: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/20.jpg)
Find the area of the shaded figure.
A =
A = bh1
2+bh
A = 1
(12)(20)2
+(36)(20)
A = + 120720
A = 840in2
20
36
+12
20
![Page 21: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/21.jpg)
Find the area of the shaded figure.
A =
9
6 + 610
c2 = a2 + b2
102 = a2 + 62
100 = a2 + 36 64 = a2
8 = a
8
A = bh1
2+bh
A = 1
(8)(6)2
+(9)(6)
A = + 2454
A = 78cm2
![Page 22: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/22.jpg)
Find the area of the shaded figure.
A = –54
3034
20
A = bh – bh
A = (54)(30) – (34)(20)
A = 1620 – 680
A = 940m2
![Page 23: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/23.jpg)
The Paint Project
This project will be done in pairs
![Page 24: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/24.jpg)
You and a friend want to go on a trip for spring break next year. Where do you want to go?
![Page 25: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/25.jpg)
Let’s assume that a plane ticket costs $1500 per person ($3000 for two). How much are hotels, food, transportation, souvenirs?
Just one problem! How will you ever afford to go? You are broke!
![Page 26: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/26.jpg)
To raise the money, you and your friend have decided to paint houses during the coming summer. Each of you will have to make $1,500 to cover the cost of the plane trip. In addition, you must include research for the extra spending money you will need for your trip.
![Page 27: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/27.jpg)
Another problem… you don’t have money for supplies to paint the houses. Your parents have decided that they will front your start-up costs if you can explain to them in detail how much everything will cost, what you will charge per house, and prove to them that you will be able to earn the money necessary to go on your spring break trip.
![Page 28: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/28.jpg)
Find out how much money you are going to need to buy the supplies to paint the houses:
Brushes and rollers…...$50
Ladders ……………... $75
Clean up materials……$30
Paint……………………$10 a gallon
The paint is now on sale for $10 per gallon. One can of paint will cover 100 square feet. You will not paint any of the roofs, doors, or windows. You will only be buying the supplies once.
![Page 29: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/29.jpg)
Luckily for you and your friend, you have been contracted to paint five identical houses and you will be able to identify the amount of paint that you will need. A sketch of one of the houses is attached. All measurements are in feet.
![Page 30: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/30.jpg)
Be thorough and creative in your proposal so that your parents are reassured and convinced of their investment in your house-painting endeavor!
![Page 31: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/31.jpg)
Step 1: Find the area of the house (complete worksheet) and how much start-up costs are to paint the 5 houses
![Page 32: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/32.jpg)
Front: Area of whole house (including windows and doors)
![Page 33: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/33.jpg)
Inside: Find the area of the windows and doors
(do not include trim!)
![Page 34: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/34.jpg)
Back: Find the total area of one house minus the windows and doors. Then multiply by 5 for five houses.
![Page 35: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/35.jpg)
Each can of paint covers 100 square feet, so divide the total square footage by 100 to find out how many cans of paint you will need.
HINT!!!! You will need 68 cans.
![Page 36: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/36.jpg)
Step 2: Research spending costs for your trip (housing, transportation, food, and extra spending money)
![Page 37: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/37.jpg)
Find the total cost of the trip Step 3:
(Step 2 + $1500 per plane ticket)
![Page 38: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/38.jpg)
Step 4: Find how much you need to charge per house to cover your trip
Start-up costs + Step 3
5
![Page 39: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/39.jpg)
Step 5: Write a proposal for your parents following the guidelines on the back of this page asking for the money for start-up costs only to paint the 5 houses.
![Page 40: 11.1 – Areas of Triangles and Parallelograms. Square: A = s 2.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649ed45503460f94be528b/html5/thumbnails/40.jpg)
11.1 723-725 3-8, 10-13, 16-18, 22-24
HW Problems
#23
A =
A = bh1
2+bh
A = 1
(9)(13)2+(18)(13)
A = + 58.5234
A = 364cm2
13
18
+9
13+
11
13
bh1
2+
1(11)(13)
2+
+ 71.5