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Solve Real-World Area and Perimeter Problems

Students apply area and perimeter formulas to solve multi-step real-world problems, such as finding the cost of fencing a garden (perimeter) or the amount of carpet needed for a room (area). Students distinguish between when to use area versus perimeter based on the context.

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Solve Real-World Area and Perimeter Problems

Grade 4 · Area and Perimeter of Rectangles · question 1 of 3

0 of 20

20 rungs. A star at the top.

A garden is 8 feet long and 3 feet wide. Which plan finds how many feet of fence are needed to go all the way around?

How it is taught

0:00 of 3:45

Area covers the inside in square units.

Perimeter goes around the outside.

Read it: Inside or around?

A garden is 8 m by 5 m. The space it covers is 8 × 5 = 40 square meters. The fence around it is 8 + 5 + 8 + 5 = 26 m.

  1. Read what the story asks about: the space inside, or the way around.
  2. For the space inside, multiply the two sides: that is the area.
  3. For the way around, add all four sides: that is the perimeter.

Area counts the squares that cover the shape, and rows times columns counts them fast.

The perimeter is the length of the edge, so it adds the sides and never multiplies them.

A missing side comes back from the rest: divide the area by the side you know, or halve the perimeter and take that side away.

Multiply the sides for the space inside. Add all four sides for the way around.

Adding one long side and one short side, 8 + 5 = 13, and calling it the way around.

That is only half the way around. 8 + 5 + 8 + 5 = 26 m.

A rectangle is 7 feet by 4 feet. Which plan finds how many feet of ribbon go all the way around it? — Join 7 and 4, then take two of those sums. Join 7 and 4, then take two of those sums: the story asks the way around, so the perimeter.

Garden 8 ft × 5 ft: fencing & grass

Here's Maya's rectangular garden. She needs fencing to go around it AND grass seed to cover the inside.

Grade 4 · Perimeter goes around, area covers inside

Look — her garden is eight feet long and five feet wide.

First question: how much fencing? Fencing goes AROUND the garden — that's perimeter.

To find the perimeter, we add up all four sides.

Eight plus five plus eight plus five equals twenty-six.

So Maya needs twenty-six feet of fencing!

Next question: how much grass seed? Grass covers the INSIDE — that's area.

To find area, we multiply length times width.

Eight times five equals forty.

Maya needs forty square feet of grass seed!

Remember: AROUND uses perimeter, in feet. INSIDE uses area, in square feet.

Now you try. Find the space inside this rectangle. What is the area?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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