Applications of Area and Perimeter

Geometry

Applications of Area and Perimeter

Name:

Teacher:

Hour:

Area Application SLOT #1

Tom and Betty are planning to paint the exterior walls of their barn (all vertical surfaces). The paint they have selected costs $24 per gallon and, according to the label, covers 150 to 300 square feet per gallon. Because the wood is very dry, they assume the paint will cover 150 square feet per gallon. How much will the project cost? (All measurements shown are in feet).

Area Application SLOT #2

Tom and Betty are planning to shingle the roof of their barn. Each shingle will cover 0.75 square feet of area. (The shingles are 1 foot by 1 foot, but they overlap by 0.25 square feet).

a)What is the total surface area of the roof of the barn? (All measurements shown are in feet).

b)Shingles are sold in packs of 500. How many packages will they need to purchase to complete the job?

c) Packs of 500 shingles sell for $165. Tom and Betty have a $1700 budget for shingles. Will they be able to pay for the shingles? How much will the shingles cost?

Area Application SLOT #3

Tom would like to raise milking cows in their new barn and Betty would like to raise sheep. After a heated argument, they decide to base their decision on which animal will earn them the most amount of money a year. Here are some statistics you need to consider:

Each cow needs approximately 35 square feet of space in the barn

Each sheep needs approximately 15 square feet of space in the barn

Each cow will earn them approximately $480 of profit per year

Each sheep will earn them approximately $170 of profit per year

Based on this data, which animal should the couple choose? Explain your reasoning. (All measurements shown are in feet).

______

Area Application SLOT #4

Jeanna’s family wants to install 1-foot-square terra cotta tiles in the entryway and kitchen, and 6-inch-square blue tiles on each bathroom floor. The terra cotta tiles cost $5 each, and the bathroom tiles cost 45¢ each. How many of each kind will they need? What will the tiles cost?

Area Application SLOT #5

Jeanna's family would like to install new carpeting in the living room and master bedroom. The carpeting costs $16 per square yard and an extra $4 per square yard for padding. How much will the new carpeting cost Jeanna's family?

Area Application SLOT #6

Area Application SLOT #7

Sabrina wants to paint the walls and ceiling of the two bedrooms, the hall, and the living room of her apartment. A gallon of TJ Base paint covers 350 ft2 and costs $19.99. A gallon of ABOT Base paint covers 400 ft2 and costs $26.39. All the ceilings are 10 ft high.

a)What is the total surface area that needs to be painted?

b)How many gallons and how much would it cost to buy the TJ Base paint?

c)How many gallons and how much would it cost to buy the ABOT Base paint?

Area Application SLOT #8

Sabrina wants to carpet the living room and hall of her apartment. She is purchasing carpet which costs $10.50 per square yard.

a)What is the total area that needs to be carpeted?

b)How much will Sabrina spend on carpet based on the price she was given above?

Area Application SLOT #9

Tammy is estimating how much she should charge for painting 148 rooms in a new motel with one coat of base paint and one coat of finishing paint. The four walls and ceiling of each room must be painted. Each room measures 14 ft by 16 ft by 10 ft high.

a)Calculate the total surface area of all the surfaces to be painted with each coat. Ignore doors and windows.

b)One gallon of base paint covers 500 square feet. One gallon of finishing paint covers 250 square feet. How many gallons of each will Tammy need for the job?

Area Application SLOT #10

The roof on Crystal’s house is formed by two congruent trapezoids and two congruent isosceles triangles as shown. She wants to put new wood shingles on her roof. Each shingle will cover 0.25 square feet of area. (The shingles are 1 foot by 1 foot, but they overlap by 0.75 square feet). How many shingles should Crystal buy?

Area Application SLOT #11

Bert’s Bigtime Bakery has baked the world’s largest chocolate cake. It is in the shape of a rectangular prism with a length of 600 cm, a width of 400 cm, and a height of180 cm. Bert wants to apply frosting to the four sides and the top. How many liters of frosting does he need if 1 liter of frosting covers about 1200 cm2? (1 liter = 100 cm2)

Area Application SLOT #12

A bundle of hardwood flooring contains 14 ½ ft2 and costs $39.90.

a)How many square feet of flooring is

needed to cover the kitchen and the

family room? Exclude the fireplace,

hearth, and tiled area.

b)You should buy 5% extra to account for waste. How many bundles of flooring should you buy?

c)What will the cost be for the flooring?

Area Application SLOT #13

Rashad wants to wallpaper the four walls of his bedroom. The room is rectangular and measures 11 feet by 13 feet. The ceiling is 10 ft high. A roll of wallpaper at the store is 2.5 feet wide and 50 feet long. How many rolls should he buy? (Wallpaper is hung from the ceiling to the floor. Ignore doors and windows).

Area Application SLOT #14

An interior designer created the kitchen plan shown. The countertop will be constructed of colored concrete.

a)What is its total surface

area of the countertop?

b)If concrete countertops 1.5 inches thick cost $85 per square foot, what will be the total cost of this countertop?

Area Application SLOT #15

The Collin's family is ready to have wall-to-wall carpeting installed. The carpeting they chose costs $12 per square yard, the padding $2 per square yard, and the installation $3 per square yard. What will it cost them to carpet the three bedrooms? (Hint: Measurements written as "17/4" represents 17 feet, 4 inches.)

Area Application SLOT #16

The bottom of a swimming pool measures 15 m by 20 m. It is to be tiled with rectangular tiles that are 50 cm by 25 cm. How many tiles will be needed?

(Hint: 1 m = 100 cm)

Area Application SLOT #17

Two drums of tar are needed to surface a driveway that is 10’3” x 23’9”. How many drums of tar will be needed to surface 3 driveways, all of which are 12’ x 30’? (Hint: 10’3” means 10 feet, 3 inches)

Area Application SLOT #18

The rectangular floor in Mark’s living room is 11 feet by 16 feet. A rectangular rug is placed in the middle of the room. What is the area of the rug?

Area Application SLOT #19

Mr. Hamoud wants to coat the ceiling, walls, and floor of a rectangular storeroom with a flame-retardant material. The dimensions of the room are 7 meters long, by 9 meters wide, by 4.5 meters high.

a)What is the total surface are of the room?

b)The flame-retardant material costs $39.95 a gallon. If one gallon covers 110 square meters, how many gallons will Mr. Hamoud need to buy?

c)How much will he spend on the gallons of flame-retardant material?

Area Application SLOT #20

Lisa is building a museum display case. The sides and bottomwill be plywood and the top will be glass. Plywood comes in4 ft-by-8 ft sheets.

Draw a picture of the plywood sheet(s) needed and determine how to place the sides and the bottom in order to purchase the least amount of plywood sheets.

Area Application SLOT #21

Tommy and Marie are planning to paint the exterior walls of their country farmhouse (all vertical surfaces).

a)What is the total surface

area to be painted?

b)The paint they like best costs $25 per gallon and covers 250 square feet per gallon. How many gallons of paint will they have to buy and how much will the paint cost?

Area Application SLOT #22

Tommy and Marie are planning to put new cedar shingles on the roof of their country farmhouse.

a)What is the total surface

area to be shingled?

b)The wood shingles cost $65 per bundle, and each bundle covers 100 square feet. How many bundles of shingles will they have to buy and how much will the shingles cost?

Area Application SLOT #23

The photo shows a Japanese police koban (station). An arch forms part of the roof and one wall. The arch is made from rectangular panels that each measure 1 meter by 0.7 meters. The arch is 11 panels high and 3 panels wide. What is the total area of the arch?

Area Application SLOT #24

Ernesto plans to build a pen for his pet iguana. What is the area of the largest rectangular pen that he can make with 100 meters of fencing?

Area Application SLOT #25

Sarah is tiling a wall in her bathroom. It is rectangular and measures 4 feet by 7 feet. The tiles are square and measure 6 inches on each side. How many tiles does Sarah need?

Area Application SLOT #26

Eduardo has designed this kite for a contest. He plans to cut the kite from a sheet of Mylar plastic and use wooden rods for the diagonals. He will connect all the vertices with string, and fold and glue the flaps over the string.

a)What is the total length

of wooden rods that

Eduardo will need to

purchase?

b)What is the total surface area that will be covered by the Mylar plastic?

c)Mylar is sold in rolls 36 inches wide. What length of Mylar will Eduardo need for this kite?

Area Application SLOT #27

Harold works at a state park. He needs to seal the redwood deck at the information center to protect the wood. He measures the deck and finds it is a kite with diagonals 40 feet and 70 feet.

a)What is the total surface area of the deck? (Hint: The kite can be split into triangles, it is symmetric.)

b)Each gallon of sealant covers 400 square feet and the sealant needs to be applied every 4 months. How many gallons should be buy to protect the deck for the next 2 years?

Area Application SLOT #28

A landscape architect is designing three trapezoid flowerbeds to wrap around three sides of a hexagonal flagstone patio, as shown.

a)What is the total area of the flowerbed?

b)The landscape architect’s fee is $100 plus $5 per square foot. Flowers cost approximately $12 per square foot. What will the flowerbed cost?

Area Application SLOT #29

Your company is producing 10,000 metal wedges as shown below. They must be plated with a thin layer of high-conducting silver. The measurements shown are in centimeters.

a)What is the total surface area

of one wedge?

b)What is the total surface area of all 10,000 wedges?

c)If silver plating costs $1 for each 200 square centimeters, what is the total cost for the silver?