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**Columbus State Community College**

Chapter 3 Section 2 Problem Solving: Area

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Problem Solving: Area Use the formula for area of a rectangle to find the area, the length, or the width. Use the formula for area of a square to find the area or the length of one side. Use the formula for area of a parallelogram to find the area, the base, or the height.

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**Difference between Perimeter and Area**

Perimeter is the distance around the outside edges of a flat shape. Area is the amount of surface inside a flat shape.

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Investigating Area 1" It will take 21 square inch pieces that measure one inch on each side to cover a rectangle that measures 7 inches long and 3 inches wide. 3" Each square piece measures one inch along each side. 1" 7" Each row contains 7 square pieces.

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Area of a Rectangle Finding the Area of a Rectangle Area of a rectangle = length • width A = l • w Remember to use square units when measuring area.

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**Finding the Area of a Rectangle**

EXAMPLE Finding the Area of a Rectangle Find the area of each rectangle. (a) 7 cm A = l • w 28 cm A = 28 cm • 7 cm A = cm2 The area of the rectangle is 196 cm2.

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**Finding the Area of a Rectangle**

EXAMPLE Finding the Area of a Rectangle Find the area of each rectangle. (b) A rectangle measuring 15 inches by 6 inches. A = l • w A = 15 in. • 6 in. 6 in. A = 90 in.2 15 in. The area of the rectangle is 90 in.2.

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**Finding the Length or Width of a Rectangle**

EXAMPLE Finding the Length or Width of a Rectangle If the area of a rectangular wall is 112 ft2 and the length is 14 ft, find the width. The value of is A is 112 ft2 and the value of l is 14 ft. A = l • w 112 ft2 = ft • w ? 14 ft 14 ft 14 ft 8 ft = w

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**Finding the Length or Width of a Rectangle**

EXAMPLE Finding the Length or Width of a Rectangle If the area of a rectangular wall is 112 ft2, and the length is 14 ft, find the width. Check To check the solution, put the width measurement on your sketch. Then use the formula. A = l • w A = ft • 8 ft 8 ft A = ft2 14 ft An area of 112 ft2 matches the information in the original problem. So 8 ft is the correct width of the wall.

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Area of a Square Finding the Area of a Square Area of a square = side • side A = s • s A = s2 Remember to use square units when measuring area.

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**Finding the Area of a Square**

EXAMPLE Finding the Area of a Square Find the area of a square table that is 4 ft on each side. Use the formula for area, A = s2. A = s2 Remember that s2 means s • s. A = s • s Replace s with 4 ft. A = 4 ft • 4 ft Multiply 4 • 4 to get 16. A = ft2 Multiply ft • ft to get ft2. The area of the table is 16 ft2.

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**Finding the Area of a Square**

EXAMPLE Finding the Area of a Square Find the area of a square table that is 4 ft on each side. Check Check the solution by drawing a square and labeling each side as 4 ft. You can multiply length ( 4 ft ) times width ( 4 ft ), as for a rectangle. So the area is 4 ft • 4 ft, or 16 ft2. This result matches the solution we got by using the formula A = s2. 4 ft 4 ft

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**Finding the Area of a Square**

CAUTION Be careful! s2 means s • s. It does not mean 2 • s. In this example s is 4 ft, so ( 4 ft )2 is 4 ft • 4 ft = 16 ft2. It is not 2 • 4 ft = 8 ft.

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**Finding the Area of a Square**

EXAMPLE Finding the Length of One Side of a Square If the area of a square floor is 36 m2, what is the length of one side of the floor? A = s2 Replace A with 36 m2. 36 m2 = s2 For now, solve by inspection. Ask, what number times itself gives 36? To get s by itself, we have to “undo” squaring of s. This is called finding the square root. 36 m2 = s • s 6 m = s 6 • 6 is 36, so 6 m • 6 m = 36 m2. The value of s is 6 m, so the length of one side of the floor is 6 m.

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**Area of a Parallelogram**

Watch as we transform this parallelogram into a rectangle. height height base base Area of a rectangle = length • width Equal areas Area of a parallelogram = base • height

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**Finding the Area of a Parallelogram**

Area of a parallelogram = base • height A = b • h Remember to use square units when measuring area.

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**Finding the Area of a Parallelogram**

EXAMPLE Finding the Area of a Parallelogram Find the area of the parallelogram. 22 ft 14 ft 9 ft Use the formula for area of a parallelogram, A = bh. A = b • h A = ft • 9 ft A = ft2 Notice that the 14 ft sides are not used in finding the area. But you would use them when finding the perimeter of the parallelogram.

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**Finding the Base or Height of a Parallelogram**

EXAMPLE Finding the Base or Height of a Parallelogram The area of a parallelogram is 256 in.2 and the base is 32 in. Find the height. ? 32 in. The value of is A is 256 in.2 and the value of b is 32 in. A = b • h 256 in.2 = in. • h 32 in. 32 in. 8 in. = h

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**Finding the Base or Height of a Parallelogram**

EXAMPLE Finding the Base or Height of a Parallelogram The area of a parallelogram is 256 in.2 and the base is 32 in. Find the height. 8 in. ? 32 in. The height of the parallelogram is 8 in. Check To check the solution, put the height measurement on the sketch. Then use the formula. A = b • h A = 32 in. • 8 in. A = in.2 An area of 256 in.2 matches the information in the original problem. So 8 in. is the correct height of the parallelogram.

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**Chapter 3 Section 2 – Completed Written by John T. Wallace**

Problem Solving: Area Chapter 3 Section 2 – Completed Written by John T. Wallace

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