Subjects
Grades
Finding Missing Measurements in Plane Figures From the Perimeter
Concept sheet | Mathematics
Secondary
1-2
Table of contents
In cases where the perimeter of a figure is known, one or more missing measurements may be sought. To solve problems related to perimeter, it is useful to know the perimeter formulas for different plane figures. Here are the steps to follow to find a missing measurement.
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Determine the formula.
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Replace the variables by the known values.
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Isolate the unknown variable.
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Answer the question.
Here are a series of examples. The first are geometry problems that have no particular context, while the last is a word problem that has a short scenario.
What is the measure of one side of a regular octagon with a perimeter of |28\ \text{cm}|?
See solution
What is the measure of the circle's radius if its circumference is |110\ \text{cm}|?
See solution
In the next examples, there are several missing measurements. Therefore, we must use algebraic expressions to represent the side measures.
What are the side measures of an isosceles triangle that has a perimeter of |16\ \text{cm}| and whose congruent sides are 2 units more than its 3rd side?
See solution
What are the side measures of a rectangle that has a perimeter of |192\ \text{cm}| and whose length measures three times the width?
See solution
Word Problem
The Cycling Grand Prix, which has been held for the past few years in Quebec City and Montreal, requires organizers to create new routes while respecting certain constraints.
This year, the race circuit must be |15\ 000\ \text{m}| long and must consist of different sections, including a climb, a descent and a straight line for the final sprint.
To respect the standards between races, the descent must be twice as long as the climb and the straight line for the sprint must be |300\ \text{m}| longer than half the climb.
What is the travelling distance for each of these 3 sections?