Calculate Perimeter: Complex Right-Angled Shape with 5, 10, and 15 Unit Measurements

Perimeter Calculation with Complex Rectilinear Shapes

Determine the perimeter of the shape below if all of its angles are equal to 90°:

5551010105551515155555

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00:00 Find the perimeter of the entire shape

Step-by-step written solution

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1

Understand the problem

Determine the perimeter of the shape below if all of its angles are equal to 90°:

5551010105551515155555

2

Step-by-step solution

To solve this problem, we'll first examine the given shape and identify the lengths of each side along its perimeter:

  • The left side is formed by three vertical segments of length 5 each, totaling 5+5+5=15 5 + 5 + 5 = 15 .
  • The top horizontal side is composed of two segments: one of length 5 and another of length 10, totaling 5+10=15 5 + 10 = 15 .
  • The bottom side is a continuous horizontal line with length 15.
  • The right vertical side has a single segment of length 10.

Let's list the lengths of the outer boundary sides to compute the total perimeter:

Perimeter P= P = Sum of all external side lengths:
P=15 P = 15 (left) +15 + 15 (top) +15 + 15 (bottom) +10 + 10 (right).
P=15+15+15+10 P = 15 + 15 + 15 + 10 .

Therefore, the solution to the problem is P=55 P = 55 .

3

Final Answer

120

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perimeter equals the sum of all outer boundary lengths
  • Method: Trace the shape's outline: 15 + 15 + 15 + 10 = 55
  • Check: Count each external side once, never internal segments ✓

Common Mistakes

Avoid these frequent errors
  • Adding internal segment lengths to perimeter
    Don't include the internal 5-unit segments that divide the shape = inflated perimeter! These segments are inside the shape, not part of the outer boundary. Always trace only the external outline of the shape.

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

How do I know which sides to include in the perimeter?

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Imagine walking around the outside of the shape. Only count the sides you would walk along! Internal lines that divide the shape don't count toward perimeter.

Why isn't the answer 30 if I see three 5s and two 10s?

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You're counting internal segments! The perimeter has four external sides: left (15), top (15), right (10), and bottom (15). Internal divisions don't add to the outer boundary.

How do I handle the step-like shape on the left side?

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The left side has three vertical segments of 5 units each, creating one continuous boundary of 5+5+5=15 5 + 5 + 5 = 15 units total.

What if I can't see all the measurements clearly?

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Look for patterns and symmetry. If one side shows 5 units and appears the same length as others, they're likely equal. Use the 90° angle clue to identify rectangular sections.

How can I double-check my perimeter calculation?

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Draw the shape on paper and physically trace the outline with your finger, adding each measurement as you go. This helps avoid counting internal segments twice!

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