Mathematics
Grade 6
15 min
Compare area and perimeter of two figures
Compare area and perimeter of two figures
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1
Introduction & Learning Objectives
Learning Objectives
Calculate the perimeter of given rectangles and squares.
Calculate the area of given rectangles and squares.
Compare the perimeters of two different geometric figures.
Compare the areas of two different geometric figures.
Explain that figures can have the same perimeter but different areas.
Explain that figures can have the same area but different perimeters.
Use appropriate units for area and perimeter when comparing figures.
Imagine you have two different gardens. 🏡 Which one needs more fencing, and which one needs more soil? 🤔
In this lesson, you will learn how to calculate and compare the area and perimeter of two different shapes, specifically rectangles and squares. Understanding these concepts helps us make practical decisions about space and...
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Key Concepts & Vocabulary
TermDefinitionExample
PerimeterThe total distance around the outside edge of a two-dimensional shape.If you walk around the edge of a rectangular park, the distance you walk is the perimeter.
AreaThe amount of surface a two-dimensional shape covers, measured in square units.The amount of grass inside a rectangular park is its area.
RectangleA four-sided flat shape with straight sides where all interior angles are right angles (90 degrees). Opposite sides are equal in length.A typical door or a piece of paper.
SquareA four-sided flat shape with straight sides where all sides are equal in length and all interior angles are right angles (90 degrees). A square is a special type of rectangle.A checkerboard square or a Rubik's Cube face.
ComparisonThe act of examining two or more things to...
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Core Formulas
Perimeter of a Rectangle
$P = 2(l + w)$
Use this formula to find the total distance around a rectangle, where 'l' is the length and 'w' is the width.
Area of a Rectangle
$A = l \times w$
Use this formula to find the amount of surface a rectangle covers, where 'l' is the length and 'w' is the width.
Perimeter of a Square
$P = 4s$
Use this formula to find the total distance around a square, where 's' is the length of one side.
Area of a Square
$A = s^2$
Use this formula to find the amount of surface a square covers, where 's' is the length of one side.
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Challenging
A farmer has 36 meters of fencing to build a rectangular pen. To give his animals the largest possible area to roam, what dimensions should he use?
A.17 m by 1 m
B.12 m by 6 m
C.9 m by 9 m
D.8 m by 10 m
Challenging
A graphic designer must create a rectangular advertisement with an area of 144 square inches. To minimize the cost of the border material, which dimensions would result in the smallest perimeter?
A.12 in by 12 in
B.16 in by 9 in
C.24 in by 6 in
D.36 in by 4 in
Challenging
Rectangle A is 20 cm long and 10 cm wide. The length of Rectangle B is 20% greater than Rectangle A's length, and its width is 10% less than Rectangle A's width. Which statement is true?
A.Rectangle B has a greater area and a greater perimeter.
B.Rectangle A has a greater area and a greater perimeter.
C.Rectangle B has a greater area but a smaller perimeter.
D.They have the same area.
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