Perimeter & Area

Problem

Composite perimeter sums boundary edges

A house-shaped figure ABCDE is built from one equilateral triangle sitting on top of a row of 3 same-size squares. The bottom of the row is 30 cm long. I need to add up the lengths of all the outside edges of ABCDE.
30 cm A B C D E
Measurement & data
Your answer
How to solve
Strategy Identify Subproblems — This is a compound shape, so the perimeter is best found by breaking it into smaller, easier subproblems: first find one square's side from the 30 cm row, then find each triangle side, then trace the outline and add only the edges that lie on the boundary. Drawing/marking the diagram makes it clear which edges are outside and which are hidden inside.
1STEP 1

Find one square's side length

The 3 congruent squares share the 30 cm bottom equally, so divide 30 by 3 to get the side of one square.

30 ÷ 3 = 10 cm
2STEP 2

Find each side of the equilateral triangle

The base runs the whole 30 cm top, and equilateral means the two slanted sides are 30 cm too.

each triangle side = 30 cm
3STEP 3

Trace the outside boundary

Outside are two 30 cm slants, two 10 cm square sides and the 30 cm bottom; the seams stay inside.

outside edges = 30, 10, 30, 10, 30 (cm)
4STEP 4

Add the boundary edges

Add the five outside edge lengths to get the perimeter.

30 + 10 + 30 + 10 + 30 = 110 cm
Answer
110 cm
The answer is a length in cm, which fits a perimeter. A quick estimate: the two triangle sides plus the bottom already give 30 + 30 + 30 = 90 cm, and the two short square sides add 20 cm more, landing at 110 cm — clearly bigger than the 30 cm bottom alone, which makes sense for a path all the way around the house shape.
Takeaway

To find the perimeter of a shape made of pieces, just walk around the outside and add up only the edges you would step along.

  • Find one square's side length
  • Find each side of the equilateral triangle
  • Trace the outside boundary
  • Add the boundary edges
Where next?
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