Measurement & data
Perimeter and circles
TEAS math
Perimeter walks the border; a circle's border is 2πr, and its inside is πr².
What this covers
P=2(l+w),C=2πr,A=πr2 (π≈3.14)- Border questions add lengths; surface questions multiply them.
- Circumference is the circle's perimeter: 2πr, or πd.
- Circle area squares the radius first, then multiplies by π.
- Keep π exact unless the exercise specifies an approximation or rounding rule.
Worked example
Worked example
A circular rug has radius 5 ft. Approximate its circumference and area using π ≈ 3.14.
- C=2π(5)≈2⋅3.14⋅5=31.4 ftThe border is 2πr. The exercise supplies the approximation for π.
- A=π(5)2≈3.14⋅52=78.5 ft2Area squares the radius and uses square units. The decimal is approximate.
Another worked example
A circle has diameter 10 cm. Find its exact circumference and area.
- r=210=5 cm,C=πd=10π cmCircumference uses diameter directly, but area needs radius.
- A=πr2=25π cm2Area squares the radius and carries square units.
A common mistake
A mistake Lemma catches
From r=210=5 cm
A=2π(5)A=π(5)2
“Area covers the inside, so it is πr² = π · 5² = 25π cm². 2πr = 2π · 5 = 10π cm is the circumference — the distance around.”
Try one
Sample problem
A garden bed measures 12 feet by 6 feet. How many feet of edging go around it? Enter the number.
P=2(12+6)Practice perimeter & circles free
No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.
Where this fits
Before this