Look at the rectangle in the figure.
Its perimeter is 30 cm.
What is its area?
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Look at the rectangle in the figure.
Its perimeter is 30 cm.
What is its area?
The perimeter of the rectangle equals the sum of all its sides, which means:
Since in a rectangle each pair of opposite sides are equal, we can say that:
This means that the two sides together equal 10, and now we'll subtract them from the perimeter and get:
This means sides AB and DC together equal 20, and since they are equal to each other, we'll divide 20 to find out how much each one equals:
Now we'll multiply side AB by side BC to find the area of the rectangle:
50 cm²
Look at the rectangle ABCD below.
Side AB is 6 cm long and side BC is 4 cm long.
What is the area of the rectangle?
Because rectangles don't have all equal sides like squares do! You know one side (height = 5), so you need to use to find the other.
It doesn't matter for area calculation! Whether you call the unknown side length or width, Area = side₁ × side₂ gives the same result.
Remember: Perimeter is around the shape (add all sides), Area is inside the shape (multiply length × width). Very different purposes!
Yes! Since you know height = 5, and there are two heights in the perimeter, that's 10 cm total. The remaining 20 cm must be the two lengths, so each length = 10 cm.
Compare to familiar objects! 50 cm² is about the size of your hand or a small book. Does that seem right for a 10×5 rectangle? Trust your intuition!
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