Pre-Algebra Unit 9 — Area and Perimeter.
This unit covers rectangles and squares, triangles and circles and circumference — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers rectangles and squares, triangles and circles and circumference — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Rectangles And Squares
Students must know the formulas for both area (A = l × w) and perimeter (P = 2l + 2w) of rectangles, and recognize that squares are rectangles where all sides are equal. Exams frequently ask students to find a missing side when area or perimeter is given, so working backwards from the formula is essential.
Key Points
- Area of a rectangle: A = length × width (units are squared, e.g., cm²)
- Perimeter of a rectangle: P = 2l + 2w or P = 2(l + w)
- For a square: A = s² and P = 4s, where s is the side length
- If area and one side are given, divide to find the missing side: missing side = A ÷ known side
A rectangle has an area of 48 cm² and a width of 6 cm. What is its perimeter?
First, find the length by dividing area by width: 48 ÷ 6 = 8 cm. Then apply the perimeter formula: P = 2(8) + 2(6) = 16 + 12 = 28 cm. Always include units — perimeter uses linear units (cm), not squared.
2 Triangles
Students must know that the area of a triangle is A = ½ × base × height, where the height is the perpendicular distance from the base to the opposite vertex — not necessarily a side of the triangle. Perimeter is simply the sum of all three sides.
Key Points
- Area of a triangle: A = ½bh (or bh ÷ 2); always use perpendicular height
- Perimeter: add all three side lengths together (P = a + b + c)
- The height may be drawn inside or outside the triangle — it must form a right angle with the base
- Exams often give a slant side as a distractor; use only the labeled base and height for area
A triangle has a base of 10 in and a height of 7 in. What is its area?
Plug into the formula: A = ½ × 10 × 7 = ½ × 70 = 35 in². The key step is multiplying base times height first, then dividing by 2. Area is always expressed in square units (in²).
3 Circles And Circumference
Students must know two formulas: circumference C = 2πr (or πd) and area A = πr². The most common exam mistake is confusing radius and diameter — always check which one is given and convert if needed (r = d ÷ 2). Use π ≈ 3.14 unless the problem says to leave the answer in terms of π.
Key Points
- Circumference (perimeter of a circle): C = 2πr = πd
- Area of a circle: A = πr² (radius must be squared, not diameter)
- Radius = diameter ÷ 2; diameter = radius × 2 — confirm which is given
- Answers left 'in terms of π' look like 36π; decimal answers use π ≈ 3.14
A circle has a diameter of 10 m. Find its circumference and area. Use π ≈ 3.14.
First, find the radius: r = 10 ÷ 2 = 5 m. For circumference: C = 2 × 3.14 × 5 = 31.4 m. For area: A = 3.14 × 5² = 3.14 × 25 = 78.5 m². Note that circumference uses linear units (m) while area uses square units (m²).
Questions, answered.
What is Area and Perimeter?
Area and Perimeter is Unit 9 of Pre-Algebra, covering rectangles and squares, triangles and circles and circumference.
How to study for Pre-Algebra Unit 9?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 25+ review questions across 5 different game modes.