Skills / Ages 11 to 14 / Math
Area of a rectangle
Finding how much flat space a rectangle covers by multiplying its length by its width, and writing the answer in square units, like 6 x 4 = 24 square feet.
Why it matters
The workbook builds every other area from this one. A triangle is half a rectangle, a leaning shape is a rectangle cut and slid over, and the outside of a box is six rectangles added together. If length times width is solid, those lessons are about seeing the rectangle, not about the arithmetic.
What it looks like when your child can do it
- Asked how much floor a 5 foot by 3 foot rug covers, your child multiplies 5 x 3 and says 15 square feet, with the word square in it.
- Your child can tell you that area counts the squares inside a shape and perimeter measures the edge around it, and knows which one a question wants.
- Shown an L-shaped floor, your child draws one straight line to cut it into two rectangles and adds their areas.
How to teach it at the kitchen table
- 01
Count squares before you multiply
On graph paper, draw a rectangle 6 squares long and 4 squares wide. Have your child count every square inside. There are 24. Area is how many of those squares it takes to cover the shape.
- 02
See the rows
Point out that the 24 squares sit in 4 rows of 6. Four rows of 6 is 4 x 6, which is 24. That is why length times width works: it counts all the rows at once.
- 03
Say the unit every time
If each square is 1 foot on a side, the answer is 24 square feet, not 24 feet. Feet measure a line. Square feet measure a patch of floor. Ask your child to say the unit out loud with every answer.
- 04
Measure something real
Use a tape measure on a rug, a garden bed or a tabletop. Round to whole feet or inches, multiply, and write the answer in square units. A real rug makes the idea stick better than a drawing does.
- 05
Cut a notched shape into rectangles
Draw a rectangle 10 across and 8 tall, then cut a notch 4 across and 3 tall out of a top corner. One straight cut makes a 10 by 5 piece and a 6 by 3 piece, so the area is 50 + 18 = 68 square units. Filling the notch in gives 80 - 12 = 68 too.
You will need: Graph paper and a pencil · A tape measure or a ruler · Sticky notes or crackers of one size
Try it together
Try 1
A garden bed is 8 feet long and 3 feet wide. How much ground does it cover?
Listen for 24 square feet, because 8 x 3 = 24. Listen for the word square in the answer. 24 feet is a length, not an area.
Try 2
A rug covers 36 square feet and is 9 feet long. How wide is it?
Listen for 4 feet, because 36 ÷ 9 = 4. Check: 9 x 4 = 36. This one runs backwards from the area to a side, and the answer is in plain feet because it is a length.
Try 3
A square patio is 12 feet on each side. What is its area?
Listen for 144 square feet, because 12 x 12 = 144. A square is a rectangle with equal sides, so the same rule works.
Try 4
A garden bed is 6 feet by 4 feet. How much edging goes around it, and how much ground does it cover?
Listen for 20 feet of edging, because 6 + 4 + 6 + 4 = 20, and 24 square feet of ground, because 6 x 4 = 24. If your child gives the same answer twice, ask which question is about the edge and which is about the inside.
Try 5
A floor is 9 feet across and 7 feet deep, with a notch cut out of one corner that is 3 feet across and 2 feet deep. How many square feet is the floor?
Listen for 57 square feet. The whole rectangle is 9 x 7 = 63, the notch is 3 x 2 = 6, and 63 - 6 = 57. Cutting it into a 9 by 5 piece and a 6 by 2 piece gives 45 + 12 = 57, the same answer.
Watch for
- Adding the sides instead of multiplying them. 6 + 4 = 10 is part of the way around, not the space inside. Ask whether the question wants the edge or the inside.
- Dropping the word square. 24 feet and 24 square feet are different kinds of answer.
If it is not there yet
- Go back to graph paper and count the squares inside small rectangles, then write the multiplication beside each one, until your child sees that rows times columns matches the count.
- Cover a small rectangle, like a book or a placemat, with sticky notes or crackers of one size and count them, so area becomes a real number of squares.
A few days of this is normal, and it is time well spent. The lesson will still be there, and it will go faster.
Where this skill comes up
Grade 6 Math Practice Workbook · Lesson 25
Area by Cutting and Rearranging
Needs it because every shape here is rebuilt from rectangles.
Grade 6 Math Practice Workbook · Lesson 28
Unfold It: Nets and Surface Area
Needs it because surface area is a sum of rectangle areas.