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What is the perimeter of ABCDE?
To solve this problem, we need to do a little bit of creative thinking. First, let’s ‘draw’ a line between A and D to see what the shape will look like.
When we draw AD, we see that we have a square since there are 4 right angles and every side is the same length of 12. From here, we can deduce that the two angles inside the newly formed triangle (2 black lines and one red dotted line) will be 60˚ , since 30˚ + 60˚ = 90.
Using our knowledge that the inside of a triangle totals 180˚, the last angle must also be 60˚. If all three angles are 60˚, we have an equilateral triangle!
Equilateral triangles also have the same length for all three sides, so the remaining two sides must also be 12.
We can now add up each length of the shape ABCDE: 12 + 12 + 12 + 12 + 12 = 60.
FAQ: I only calculated AB + BC + CD + DE. Why doesn't the question ask for the perimeter of ABCDEA?
When we say "perimeter," it refers to the combined length of all sides of a shape. We can only get the perimeter of a closed space.
At the same time, when we refer to a shape using the names of its points (e.g. ABCDE), it refers to the whole shape, including all sides. We don't need to include any point twice in the name :-)
Watch the lessons below for more detailed explanations of the concepts tested in this question. And don't worry, you'll be able to return to this answer from the lesson page.