AREA PROBLEMS

AREA PROBLEMSLETS USE POLYNOMIALS Area Problem SolvingAn oil painting is 10 cm longer than it is wide and is bordered on all sides by a 3 cm wide frame. If the area of the frame alone is 402 cm2, what are the dimensions of the painting?

What are our problem solving strategies????Area Problem SolvingAn oil painting is 10 cm longer than it is wide and is bordered on all sides by a 3 cm wide frame. If the area of the frame alone is 402 cm2, what are the dimensions of the painting?

STEP 1 : What is your unknown? What is the question asking for?STEP 2: State your knownsSTEP 3: SolveArea Problem Solving Example 1An oil painting is 10 cm longer than it is wide and is bordered on all sides by a 3 cm wide frame. If the area of the frame alone is 402 cm2, what are the dimensions of the painting?

STEP 1: What is your unknown? What is the question asking for?

Dimensions of the painting.x = widthx+10 = lengthxxx+10Area Problem Solving Example1An oil painting is 10 cm longer than it is wide and is bordered on all sides by a 3 cm wide frame. If the area of the frame alone is 402 cm2, what are the dimensions of the painting?

STEP 1: Unknown is width and length of painting, width = x, length = x + 10

STEP 2 : State your knownsArea = (length)(width)xxx+10Area Problem Solving Example 1An oil painting is 10 cm longer than it is wide and is bordered on all sides by a 3 cm wide frame. If the area of the frame alone is 402 cm2, what are the dimensions of the painting?

STEP 1: Unknown is width and length of painting, width = x, length = x + 10

STEP 2 : State your knownsArea = (length)(width)Painting: width = x, length = x+10Painting + Frame: width = x + 6, length = x + 16xxx+10x+6x+10+6 or x +163cm3cm3cm3cmArea Problem Solving Example 1An oil painting is 10 cm longer than it is wide and is bordered on all sides by a 3 cm wide frame. If the area of the frame alone is 402 cm2, what are the dimensions of the painting?

STEP 1: Unknown is width and length of painting, width = x, length = x + 10

STEP2: State your knownsArea = (length)(width)Painting: width = x, length = x+10Frame: width = x + 6, length = x + 16Area of frame = 402 cm2xxx+10x+6x+10+6 or x +163cm3cm3cm3cmArea Problem Solving Example 1xxx+10x+6x+10+6 or x +163cm3cm3cm3cmSOLVE Width = 25.5cmLength = 35.5cmxxx+10x+6x +16Area Problem Solving Example 2A rectangle is twice as long as it is wide. If its length is decreased by 4 and its width is decreased by 2, its area is decreased by 24. Find its original dimensions.

STEP 1 : What is your unknown? What is the question asking for?STEP 2: State your knownsSTEP 3: Solve

Area Problem Solving Example 2A rectangle is twice as long as it is wide. If its length is decreased by 4 and its width is decreased by 2, its area is decreased by 24. Find its original dimensions.

STEP 1 : What is your unknown? What is the question asking for?Dimensions of original rectanglewidth = x, length = 2x

x2xArea Problem Solving Example 2x2xx - 22x - 4Area Problem Solving Example 2x2xx - 22x - 4SOLVEDimensions of original rectanglewidth = x, length = 2xWidth = 4, Length = 8AREA PROBLEMS Part II15Area Problem Solving #1A rectangle is three times as long as it is wide. If its length and width are both decreased by 2 cm, its area is decreased by 36 cm2. Find its original dimensions.

STEP 1 : What is your unknown? What is the question asking for?Dimensions of original rectanglewidth = x, length = 3x

x3xArea Problem Solving #1x3xx - 23x - 2Area Problem Solving #1x3xx - 23x - 2SOLVEDimensions of original rectanglewidth = x, length = 2xWidth = 5, Length = 15LETS USE POLYNOMIALS Area Problem SolvingA house has two rooms of equal area. One room is square and the other room is a rectangle 4 ft narrower and 5 ft longer than the square one. Find the area of each room

STEP 1 Area of square room Area of rectangle roomSo, I will need dimensions of each, length and widthArea Problem Solving #1A rectangle is three times as long as it is wide. If its length and width are both decreased by 2 cm, its area is decreased by 36 cm2. Find its original dimensions.

STEP 1 Area of square room Area of rectangle roomSo, I will need dimensions of each, length and width

xxx-4x+5Area Problem Solving #1A rectangle is three times as long as it is wide. If its length and width are both decreased by 2 cm, its area is decreased by 36 cm2. Find its original dimensions.

STEP 1 Area of square room Area of rectangle roomSo, I will need dimensions of each, length and width

STEP 2 Area = (length)(width)

Area = x2Area = (x+5)(x-4)xxx-4x+5Area Problem Solving #1A rectangle is three times as long as it is wide. If its length and width are both decreased by 2 cm, its area is decreased by 36 cm2. Find its original dimensions.

STEP 1 Area of square room Area of rectangle roomSo, I will need dimensions of each, length and width

STEP 2 - Area = (length)(width)

Area = x2Area = (x+5)(x-4)

AREAS ARE EQUAL, SO x2=(x+5)(x-4)xxx-4x+5SOLVEAREA of each room = 400 ft2

Dimensions of square roomwidth = 20 ft, length = 20 ftDimensions of rectangular roomWidth = 16 ft, Length = 25 ft