Columbus State Community College Chapter 3 Section 2 Problem Solving: Area

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.

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.

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.

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.

Finding the Area of a Rectangle EXAMPLE 1 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 = 196 cm2 The area of the rectangle is 196 cm2.

Finding the Area of a Rectangle EXAMPLE 1 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.

Finding the Length or Width of a Rectangle EXAMPLE 2 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 = 14 ft • w ? 14 ft 14 ft 14 ft 8 ft = w

Finding the Length or Width of a Rectangle EXAMPLE 2 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 = 14 ft • 8 ft 8 ft A = 112 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.

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.

Finding the Area of a Square EXAMPLE 3 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 = 16 ft2 Multiply ft • ft to get ft2. The area of the table is 16 ft2.

Finding the Area of a Square EXAMPLE 3 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

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.

Finding the Area of a Square EXAMPLE 4 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.

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

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

Finding the Area of a Parallelogram EXAMPLE 5 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 = 22 ft • 9 ft A = 198 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.

Finding the Base or Height of a Parallelogram EXAMPLE 6 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 = 32 in. • h 32 in. 32 in. 8 in. = h

Finding the Base or Height of a Parallelogram EXAMPLE 6 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 = 256 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.

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