7.G.4: Area and Circumference of a Circle
Also written as 7.G.B.4 and CCSS.MATH.CONTENT.7.G.B.4 · Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
The Official Wording
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Common Core State Standards, Grade 7, Geometry · Read it at the source · Checked October 14, 2026
What 7.G.4 Means in Plain English
Seventh graders use C = πd and A = πr², with 3.14 for π. A garden 10 ft across needs 31.4 ft of edging and covers 78.5 ft², and students can say which question asks for distance around and which asks for space inside.
They also explain why the formulas connect: cut a circle into thin wedges, lay them into a near-rectangle, and its area is half the circumference times the radius, which is πr². 8th grade builds cylinder and cone volume on πr² (8.G.9).
7.G.4 I Can Statements
- I can find a circle’s circumference from its radius or diameter.
- I can find a circle’s area using A = πr².
- I can explain why rearranged wedges give the area formula.
7.G.4 Worked Example
A round garden bed: the edging is the circumference, the soil is the area, and a ring of wedges shows why the two formulas belong together.
A circular garden is 10 ft across. How many feet of edging go around it, and how much ground does it cover? Use 3.14 for π.
- Ten feet across is the diameter. The radius is half of it.r = 10 ÷ 2 = 5 ft
- Edging goes around the outside, so it is the circumference.C = πd = 3.14 × 10 = 31.4 ft
- Ground covered is area. Square the radius first, then multiply by π.A = πr² = 3.14 × 5² = 3.14 × 25 = 78.5 ft²
- Why πr² works: cut the circle into 16 thin wedges and lay them tip up, tip down. They make a near-rectangle as long as half the circumference and as tall as the radius.A ≈ ½C × r = 15.7 × 5 = 78.5 ft²
Check it: Box the circle in a 10 by 10 square, 100 ft²: the circle fills a little over ¾ of it, and 78.5 is. The edging is a little more than 3 diameters, 30 ft, and 31.4 is.
Common Mistakes with 7.G.4
Putting the diameter into πr²
A = 3.14 × 10² = 314 ft²
Try this: Halve the diameter first and write r = 5 above the formula; 314 ft² is the area of a circle 20 ft across.
Doubling the radius instead of squaring it
A = 3.14 × 5 × 2 = 31.4 ft²
Try this: Write r² as r × r, so 5 × 5 = 25, before multiplying by 3.14; doubling the radius gives the diameter, not its square.
Swapping area and circumference
A fence around a pen with a 5 ft radius is 78.5 ft long
Try this: Ask whether the answer is a length or a covering: fences and edging are circumference in feet, lawns and rugs are area in square feet.
Where 7.G.4 Fits
Practice 7.G.4
Quick Check
- A bike wheel has a diameter of 20 in. How far does it roll in one full turn? Use 3.14 for π.
- Find the area of a circle with a radius of 3 m. Use 3.14 for π.
- A circle’s circumference is 31.4 cm. What is its area? Use 3.14 for π.