Steply

Perimeter and area

Geometry · 26 problems, easy to harder

▶ Watch the first one solved

How we do it

  1. What area means
  2. Length times width
  3. Check

The steps for Area of rectangle 8 by 5. Every solution names its steps, so you always know what comes next.

Worked examples

Area of rectangle 8 by 5 Easy

The question

Question: find the area of a rectangle 8 long and 5 wide.

1 What area means

Area is how much space is inside.

We count the 1 by 1 squares that fit.

One row has 8 squares.

There are 5 rows.

2 Length times width

So the area is length times width: A = length × width.

Squares in a row, times the rows.

A = length × width

Now put the numbers in: length = 8 and width = 5.

A = 8 × 5

8 times 5 is 40.

So the area is 40 square units.

A = 40

3 Check

Let's check: count row by row.

5 rows of 8 squares.

8 + 8 + 8 + 8 + 8 = 40

We get 40 again.

So the area is right!

Let's look back.

First: what area means.

Then: length times width.

Last: check.

Answer
A = 40

▶ Watch it solved

Area of circle radius 3 Medium

The question

Question: find the area of a circle with radius 3.

1 Use the rule

π is a special number for circles.

It is about 3.14.

The area of a circle is π times the radius squared: A = π × r².

So we write A = π × r².

A = π × r2

Now put the numbers in: r = 3.

A = π × 32

3² means 3 times 3.

That is 9.

32 = 3 × 3 = 9

So A = π × 9.

A = π × 9

We write it as 9π.

We keep π in the answer.

That is the exact answer.

A = 9π

2 About how much

To see about how much, put 3.14 for π.

A ≈ 9 × 3.14

9 times 3.14 is 28.26.

So the area is about 28.26 square units.

A ≈ 28.26

Let's look back.

First: use the rule.

Last: about how much.

Answer
A ≈ 28.26

▶ Watch it solved

Area of circle radius 7 cm Harder

The question

Question: find the area of a circle with radius 7 cm.

1 Use the rule

π is a special number for circles.

It is about 3.14.

The area of a circle is π times the radius squared: A = π × r².

So we write A = π × r².

A = π × r2

Now put the numbers in: r = 7.

A = π × 72

7² means 7 times 7.

That is 49.

72 = 7 × 7 = 49

So A = π × 49.

A = π × 49

We write it as 49π.

We keep π in the answer.

That is the exact answer.

A = 49π cm2

2 About how much

To see about how much, put 3.14 for π.

A ≈ 49 × 3.14

49 times 3.14 is 153.86.

So the area is about 153.86 cm².

A ≈ 153.86 cm2

Let's look back.

First: use the rule.

Last: about how much.

Answer
A ≈ 153.86 cm2

▶ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. area of rectangle 8 by 5
    Answer
    A = 40
  2. perimeter of rectangle 8 cm by 5 cm
    Answer
    P = 26 cm
  3. area of square side 6
    Answer
    A = 36
  4. perimeter of square side 7 m
    Answer
    P = 28 m
  5. area of triangle base 10 height 6
    Answer
    A = 30
  6. area of rectangle 12 m by 3 m
    Answer
    A = 36 m2
  7. perimeter of triangle 3, 4, 5
    Answer
    P = 12
  8. area of triangle base 8 cm height 5 cm
    Answer
    A = 20 cm2

Medium

  1. area of circle radius 3
    Answer
    A ≈ 28.26
  2. area of circle diameter 10 cm
    Answer
    A ≈ 78.5 cm2
  3. circumference of circle radius 3
    Answer
    C ≈ 18.84
  4. circumference of circle diameter 8 m
    Answer
    C ≈ 25.12 m
  5. area of L shape 10 by 8 cut 4 by 3
    Answer
    A = 68
  6. area of L shape 12 by 9 cut 5 by 4
    Answer
    A = 88
  7. perimeter of triangle 3, 4, 9
    Answer
    4 + 3 < 9 impossible
  8. area of rectangle 15 by 4
    Answer
    A = 60
  9. perimeter of rectangle 14 m by 9 m
    Answer
    P = 46 m

Harder

  1. area of circle radius 7 cm
    Answer
    A ≈ 153.86 cm2
  2. area of L shape 20 m by 15 m cut 8 m by 6 m
    Answer
    A = 252 m2
  3. area of triangle base 9 height 7
    Answer
    A = 31.5
  4. area of rectangle 2.5 by 4
    Answer
    A = 10
  5. area of triangle base 3.5 height 4
    Answer
    A = 7
  6. area of circle radius 1.5 m
    Answer
    A ≈ 7.07 m2
  7. circumference of circle diameter 7 cm
    Answer
    C ≈ 21.98 cm
  8. perimeter of triangle 4.5, 6, 7.5
    Answer
    P = 18
  9. area of L shape 10 by 8 cut 4.5 by 3
    Answer
    A = 66.5