Mathematics
Grade 10
15 min
Area of rectangles and squares
Area of rectangles and squares
What you'll learn
- Identify at least 3 equivalent ratios for a given ratio using multiplication or division with 80% accuracy.
- Solve ratio problems involving finding a missing value in an equivalent ratio using cross-multiplication or scaling, and correctly answer 3 out of 4 problems.
- Explain, in writing, why two ratios are or are not equivalent, using mathematical vocabulary like 'multiply', 'divide', and 'same factor' with at least 70% accuracy based on a rubric.
- Apply the concept of equivalent ratios to solve real-world problems involving proportions, such as scaling a recipe up or down, and get the correct answer in at least 2 out of 3 word problems.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the area of rectangles and squares when dimensions are expressed as algebraic expressions.
Solve for unknown dimensions of a rectangle or square given its area and one other dimension, potentially involving solving linear or quadratic equations.
Calculate the area of a rectangle or square defined by vertices on a Cartesian plane.
Apply area formulas to solve multi-step word problems, including those involving unit conversions or composite shapes.
Use the Pythagorean theorem to find a missing dimension of a rectangle given its diagonal and one side, and then calculate its area.
Formulate a simple proof related to the area of rectangles or squares.
How does a GPS calculate the area of a rectangular park from satellite data? 🛰️ It all comes down to...
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Key Concepts & Vocabulary
TermDefinitionExample
AreaThe measure of the two-dimensional space enclosed by a shape. It is always expressed in square units (e.g., cm², m², square units).A floor tile that is 1 foot by 1 foot has an area of 1 square foot.
RectangleA quadrilateral with four right angles (90°). Opposite sides are equal in length and parallel.A standard sheet of A4 paper, a smartphone screen, or a door.
SquareA special type of rectangle where all four sides are equal in length. It also has four right angles.A single square on a chessboard or a standard wall tile.
DimensionsThe measurements that define the size of a shape. For a rectangle, these are its length and width. For a square, it is the side length.A rectangle might have dimensions of 5 meters by 3 meters.
Cartesian PlaneA two-dimensional coordinat...
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Core Formulas
Area of a Rectangle
A = l \times w
The area (A) of a rectangle is found by multiplying its length (l) by its width (w). Ensure both dimensions are in the same unit before multiplying.
Area of a Square
A = s^2
The area (A) of a square is found by squaring its side length (s). This is a special case of the rectangle formula where l = w = s.
Pythagorean Theorem (for finding dimensions)
l^2 + w^2 = d^2
In a rectangle, the length (l), width (w), and diagonal (d) form a right-angled triangle. This theorem can be used to find a missing side length if the other side and the diagonal are known.
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Challenging
A rectangle has a perimeter of 34 meters and an area of 60 square meters. What are its dimensions?
A.Length = 10 m, Width = 6 m
B.Length = 15 m, Width = 4 m
C.Length = 12 m, Width = 5 m
D.Length = 20 m, Width = 3 m
Challenging
The length of a rectangular plot is increased by 20% and its width is decreased by 10%. What is the net percentage change in the area of the plot?
A.10% increase
B.8% increase
C.12% increase
D.2% decrease
Challenging
Given a square with side length 'a' and a smaller square with side length 'b'. The difference in their areas, a² - b², can be represented geometrically by the area of a specific rectangle. What are the dimensions of this rectangle?
A.Length = (a - b), Width = (a + b)
B.Length = a, Width = (a - b)
C.Length = (a + b), Width = (a + b)
D.Length = 2a, Width = 2b
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Frequently asked questions
What grade level is "Area of rectangles and squares"?
Area of rectangles and squares is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Area of rectangles and squares?
You'll be able to: Identify at least 3 equivalent ratios for a given ratio using multiplication or division with 80% accuracy; Solve ratio problems involving finding a missing value in an equivalent ratio using cross-multiplication or scaling, and….
Is "Area of rectangles and squares" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Area of rectangles and squares?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.