# Area of rectangles - free lesson with a video

This lesson contains teaching and lots of varied exercises about the area of rectangles, common units of area, two-part rectangles and the distributive property, and shapes composed of rectangular areas. It best suits 4th or 5th grade.

The video below shows you some varied exercises tying in with the area of rectangles.

Area is always measured in squares of some size. We use the superscript “2” with a unit of length to indicate the “squaring”. For example, 120 cm2 means 120 square centimeters.
 The area of this square is 1 square centimeter, or 1 cm2.
 Each tiny square has an area of 1 square millimeter, or 1 mm2. The area of the whole square is 10 mm × 10 mm = 100 mm2.

 You can use multiplication to find how many square inches this rectangle covers: 2 in. × 4 in. = 8 in2.

 The area of this square is 1 mi. × 1 mi. = 1 square mile, or 1 mi2

 If no particular unit of length is given for the sides of a rectangle, we just use the word “unit” for the side lengths. The area is then 7 units × 4 units = 28 square units.
 If the figure is some other shape than a rectangle, we will still use little squares to measure its area. It is just more difficult to find out how many little squares it covers, and we may have to use partial (fractional) squares as well.

1. Write a multiplication to calculate the area of these rectangles. Include the units!

 a.   A = _______ × _______    = ________________ b.   A = _______ × _______    = ________________ c. A = _______ × _______    = ________________

2. Find the missing measurements.

 a. b. c.

3. Write a multiplication with an unknown (an equation) for the area. Then solve.

 a.   ________________________________________________________ b.   ____________________________ ____________________________

4. Write a multiplication with an unknown (an equation) for the area. Then solve.

a. The area of a rectangle is 45 m., and its one side measures 9 m.
How long is the other side (s)?

________________________________________________________

b. The area of a rectangular field is 1,800 ft2, and its one side measures 60 ft.
How long is the other side (s)?

________________________________________________________

 5. This is the bottom plan for a doghouse. In the grid, the side of each      little square is 6 inches in reality.     a. What is the area of the doghouse in square inches?       b. Figure out the side lengths in feet.         Then calculate the area in square feet.

If we think of this rectangle as two rectangles,
we can write its area as  3 × 3   +   3 × 5.

But if we think of it as one rectangle with side lengths 3 units
and (3 + 5) units, then we can write its area as  3 × (3 + 5).

So, thinking of it as one rectangle or two rectangles, we get:

 3 × (3 + 5) = 3 × 3 + 3 × 5 area of the whole rectangle area of the first part area of the second part

3

3 + 5

6. Write a number sentence for the total area, thinking of one rectangle or two.

 a. ___ ×  ( ___ + ___ ) = ___ × ___ + ___ × ___ area of the whole rectangle area of the first part area of the second part
 b. ___ ×  ( ___ + ___ ) = ___ × ___ + ___ × ___ area of the whole rectangle area of the first part area of the second part

7. This is a plan for a two-part clubhouse.

a. Write a multiplication & addition sentence for the total area,
thinking of one rectangle or two. Solve it.

A = ________ × ( ________ + ________ )

= ________ ×________  +  ________ ×________

= ______________________________________

b. How much larger in area is the part A2 than the part A1?

8. On a separate paper, draw these squares.

a. a square with an area of 4 square inches. How long is its side? ______________

b. a square with an area of 9 cm2. How long is its side? ______________

c. a square with an area of 1 square foot. How long is its side? ______________

9. Write a number sentence (use multiplication, addition, and/or subtraction) for the area of each figure.

 a. b.

10. The second floor of a doll house has three rooms. One room measures 20 cm by 25 cm,
the middle room is 40 cm by 25 cm, and the third one is 20 cm by 25 cm.

a. Draw a sketch of the second floor.

b. Find its area.

11. Draw two different L-shapes with an area of at least 20 square units. Write a number sentence for
their areas.

 a.  _________________________________ _________________________________ b.  _________________________________ _________________________________

12. The picture shows a rectangular piece of land with a house in the middle.
The plot of land measures 48 ft by 48 ft, and the house is 30 ft by 20 ft.

What is the area of the lawn?

13. Find the areas of the shaded figures.

 a. b.

This lesson is taken from my book Math Mammoth Geometry 1.

#### Math Mammoth Geometry 1

A self-teaching worktext for 4th-5th grade that covers angles, triangles, quadrilaterals, cirlce, symmetry, perimeter, area, and volume. Lots of drawing exercises!