11.1 – Areas of Triangles and Parallelograms

Square:

A = s2

Rectangle:

A = bh

Parallelogram:

A = bh

Note: The height is the perpendicular distance between the parallel sides

Triangle:

A bh1

2

Note: The height is the perpendicular line

Triangle:

If two polygons are _______________, then they have the same ____________.

congruentareas

Find the area of the shape.

A = s2

A = (11)2

A = 121 u2

Find the area of the shape.

A = bh

A = (9)(3)

A = 27 u2

Find the area of the shape.

A = bh

A = (16)(10)

A = 160 u2

12

Find the area of the shape.

A bh1

2

A1

(8)(16)2

A 4(16)

A u264

24

Find the area of the shape.

A = bh

A = (12)(8)

A = 96 u2

10

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

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

Find the value of x.

A = bh

576 = x 18

32in = x

Find the value of x.

A bh1

2

x1

70 (10)2

x70 5

cm x14

Find the value of x.

A = bh

104 = 16x

6.5in = x

The area of a region is the _______ of the areas of its nonoverlapping parts.

sum

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

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

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

Find the area of the shaded figure.

A = –54

3034

20

A = bh – bh

A = (54)(30) – (34)(20)

A = 1620 – 680

A = 940m2

The Paint Project

This project will be done in pairs

You and a friend want to go on a trip for spring break next year. Where do you want to go?

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!

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.

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.

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.

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.

Be thorough and creative in your proposal so that your parents are reassured and convinced of their investment in your house-painting endeavor!

Step 1: Find the area of the house (complete worksheet) and how much start-up costs are to paint the 5 houses

Front: Area of whole house (including windows and doors)

Inside: Find the area of the windows and doors

(do not include trim!)

Back: Find the total area of one house minus the windows and doors. Then multiply by 5 for five houses.

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.

Step 2: Research spending costs for your trip (housing, transportation, food, and extra spending money)

Find the total cost of the trip Step 3:

(Step 2 + $1500 per plane ticket)

Step 4: Find how much you need to charge per house to cover your trip

Start-up costs + Step 3

5

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.

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