Chapter 10
Perimeter and Area
Imagine planning a garden with a fixed amount of fencing. You sketch several outlines and wonder how much room each would leave for plants. Measuring the edges feels familiar, but judging the space inside raises a different question. Perimeter and area give us a language for thinking carefully about both parts of the design. What evidence would convince you that one shape has more space than another, especially when neither looks like a rectangle?
What You'll Explore
6 lessons.
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What makes a triangle's area calculation convincing, even when the triangle is long, narrow, or tilted? Familiar rectangles offer a starting point for investigating the geometric reasons behind area measurements and the role of height.
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Trapezoids, rhombi, and kites all have four sides, but which measurements matter when you want their areas? Their diagrams invite a closer look at the measurements and geometric conditions an area calculation depends on.
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Can you compare two triangular regions without calculating both areas separately? Shared measurements and partitions within a larger triangle provide several ways to explore that question.
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Hexagonal floor tiles have a familiar outline, but what measurements would help you decide how much space one covers? A closer look at the center, sides, and distances within a regular polygon raises questions about which information matters.
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Picture a floor plan with an inward corner and an open courtyard: how much flooring belongs inside, and which edges need trim? Composite and shaded regions make you decide exactly what is being measured before starting a calculation.
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Does enlarging a design change its area in the way you would expect from its side lengths? The same design can lead to different questions when you are given lengths, perimeters, or areas.