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

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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

9. 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.

10. 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.

11. 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.

12. 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

13. 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.

14. 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.

15. 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

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

17. 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.

18. 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

19. 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.

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