TEAS Ready📏 Math · Measurement and Data · Lesson 5 of 7 · 6 min
Perimeter, area and circles
📐 Fencing a garden is perimeter; carpeting a room is area. Mixing them up is the most common geometry mistake.
💡 Key idea
Perimeter goes around (units), area fills inside (square units); for circles C = 2πr and A = πr² with π ≈ 3.14.
🧠 The idea
PERIMETER is the distance around a shape: add all the side lengths. For a rectangle, P = 2l + 2w. AREA is the space inside, measured in square units. Rectangle: A = l × w. Square: A = s². Triangle: A = ½ × b × h, where the height is perpendicular to the base. For a CIRCLE, the radius r runs from the center to the edge and the diameter d = 2r. CIRCUMFERENCE (the perimeter of a circle) is C = 2πr = πd, and area is A = πr². On the TEAS use π ≈ 3.14. For an odd shape, split it into rectangles and triangles, find each area, and add. Check units: perimeter and circumference are in plain units (ft), area in square units (ft²). If a problem gives the diameter, halve it before using A = πr².
✏️ Worked example
A circular rug has a diameter of 10 ft. Find its area and its circumference.
Step 1: Radius = diameter ÷ 2 = 10 ÷ 2 = 5 ft.
Step 2: Area = πr² = 3.14 × 5² = 3.14 × 25 = 78.5 ft².
Step 3: Circumference = πd = 3.14 × 10 = 31.4 ft.
Answer: area 78.5 square feet; circumference 31.4 feet.
📌 Takeaways
- Rectangle A = l × w, P = 2l + 2w; triangle A = ½bh.
- Circle C = 2πr = πd, A = πr², π ≈ 3.14.
- Given a diameter, halve it before squaring.
📖 Terms in this lesson
Perimeter: The total distance around a flat shape; for example, a 3 ft by 5 ft rectangle has a perimeter of 16 ft.
Area: The amount of surface a flat shape covers, in square units; for example, a 3 ft by 5 ft rectangle has an area of 15 sq ft.
Circumference: The distance around a circle: C = πd = 2πr; for example, a circle with a 10 cm diameter has a circumference of about 31.4 cm.
✅ Check yourself
Question 1 of 3
A rectangular room is 8 ft long and 5 ft wide. What is its area?
- 80 ft²
- 40 ft²
- 13 ft²
- 26 ft²
Show the answer and rationale
Answer: B
Area = length × width = 8 × 5 = 40 ft². The value 26 is the perimeter (2 × 8 + 2 × 5), 13 is just 8 + 5, and 80 doubles the area.
Question 2 of 3
What is the circumference of a circle with a radius of 3 cm? (Use π ≈ 3.14.)
- 9.42 cm
- 18.84 cm
- 28.26 cm
- 113.04 cm
Show the answer and rationale
Answer: B
C = 2πr = 2 × 3.14 × 3 = 18.84 cm. The value 9.42 forgets the 2, 28.26 is the area (πr²), and 113.04 squares the diameter (3.14 × 6²), mixing up the circumference and area formulas.
Question 3 of 3
A triangle has a base of 10 in and a height of 6 in. What is its area?
- 60 in²
- 30 in²
- 120 in²
- 16 in²
Show the answer and rationale
Answer: B
A = ½ × b × h = ½ × 10 × 6 = 30 in². Sixty forgets the ½, 16 adds the base and height, and 120 multiplies by 2 instead of by ½.
The full lesson with XP and a streak in the app. No account needed.