Formulas for Area
The formulas for area of squares and rectangles are A = s squared for a square and A = l times w for a rectangle, where all measurements must be in the same units and the result is in square units. A rectangle 6 inches by 4 inches has an area of 24 square inches, and a square with 5-mile sides has an area of 25 square miles. This Grade 7 math skill from Saxon Math, Course 2 establishes the foundational area formulas that extend to all other polygons and is essential for real-world applications in construction, flooring, land measurement, and design.
Key Concepts
Property To find the area of a square or rectangle, use these formulas: $$ \text{Area of a square} = \text{side} \times \text{side} \quad A = s^2 $$ $$ \text{Area of a rectangle} = \text{length} \times \text{width} \quad A = lw $$.
Examples A rectangle with length 6 in. and width 4 in. has an area of $A = 6 \text{ in.} \cdot 4 \text{ in.} = 24 \text{ in.}^2$. A square with a side length of 5 miles has an area of $A = (5 \text{ mi})^2 = 25 \text{ mi}^2$. A square with a perimeter of 20 cm has sides of $20 \div 4 = 5$ cm, so its area is $A = (5 \text{ cm})^2 = 25 \text{ cm}^2$.
Explanation Finding a shape's area is like calculating how many one foot square tiles would cover its entire surface. Instead of counting each tile individually, you can use a simple trick: multiply the length by the width. For a perfect square where all sides are equal, you just multiply the side length by itself. It's the ultimate shortcut for measuring flat spaces!
Common Questions
What is the formula for the area of a rectangle?
The area of a rectangle is A = length times width (A = lw). For a rectangle 6 inches long and 4 inches wide, A = 6 times 4 = 24 square inches.
What is the formula for the area of a square?
The area of a square is A = side times side = side squared (A = s squared). For a square with side 5 miles, A = 5 squared = 25 square miles.
Why is area measured in square units?
Area measures two-dimensional space. Each square unit is a square with side length 1 in the given unit. The area tells you how many unit squares fill the shape.
What is the difference between perimeter and area?
Perimeter is the distance around the outside of a shape, measured in linear units. Area is the amount of surface inside the shape, measured in square units.
When do students learn area formulas for squares and rectangles?
These formulas are introduced in Grade 3-4 and are reinforced throughout Grade 7. Saxon Math, Course 2 reviews them in Chapter 3 before extending to more complex shapes.
How do I apply the area formula to a real-world problem?
Identify the shape, measure or identify the length and width (or side), apply the formula, and include square units in the answer. For flooring a room 12 ft by 10 ft: A = 12 times 10 = 120 square feet.
How do area formulas for rectangles extend to parallelograms and triangles?
The parallelogram formula (A = base times height) has the same structure as the rectangle formula. The triangle formula (A = 1/2 times base times height) is half of the parallelogram area.