Calculate Rectangle Area: Using Given Dimensions 8 and 17

Rectangle Area with Pythagorean Theorem

Look at the following rectangle:

AAABBBCCCDDD178

BC = 8

BD = 17

Calculate the area of the rectangle ABCD.

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1

Understand the problem

Look at the following rectangle:

AAABBBCCCDDD178

BC = 8

BD = 17

Calculate the area of the rectangle ABCD.

2

Step-by-step solution

We will find side DC by using the Pythagorean theorem in triangle DBC:

BC2+CD2=BD2 BC^2+CD^2=BD^2

Let's substitute the known data:

82+CD2=172 8^2+CD^2=17^2

CD2=28964=225 CD^2=289-64=225

Let's take the square root:

CD=15 CD=15

Now we have the length and width of rectangle ABCD and we'll calculate the area:

15×8=120 15\times8=120

3

Final Answer

120

Key Points to Remember

Essential concepts to master this topic
  • Pythagorean Rule: In right triangles, a2+b2=c2 a^2 + b^2 = c^2
  • Technique: Use diagonal as hypotenuse: 82+CD2=172 8^2 + CD^2 = 17^2
  • Check: Verify area calculation: 15 × 8 = 120 square units ✓

Common Mistakes

Avoid these frequent errors
  • Using diagonal as a side for area calculation
    Don't multiply diagonal × side = 17 × 8 = 136 for area! The diagonal is the hypotenuse, not a rectangle side, giving wrong area. Always find the missing side first using Pythagorean theorem, then multiply length × width.

Practice Quiz

Test your knowledge with interactive questions

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?
666444AAABBBCCCDDD

FAQ

Everything you need to know about this question

Why can't I just use the diagonal to find the area?

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The diagonal isn't a side of the rectangle! Area requires length × width, not diagonal × side. The diagonal helps you find the missing side using the Pythagorean theorem.

How do I know which sides form the right triangle?

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Look for the diagonal - it's always the hypotenuse! The two sides that meet at a corner (like BC and CD) are the legs of the right triangle formed by the diagonal.

What if I get a negative number when taking the square root?

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Check your arithmetic! In geometry problems, side lengths are always positive. If you get negative under the square root, you made a calculation error.

Do I always need the Pythagorean theorem for rectangle problems?

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Only when you're given a diagonal and need to find a missing side. If you already know both length and width, just multiply them directly!

How can I check if my side length is correct?

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Substitute back into the Pythagorean theorem: 82+152=64+225=289=172 8^2 + 15^2 = 64 + 225 = 289 = 17^2

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