Finding Missing Measurements in Plane Figures from their Area

Concept sheet | Mathematics

Secondary

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Word Problem
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Occasionally, you may be asked to find one or more missing measurements from the perimeter or area of a figure. To solve problems related to area, it is useful to know the area formulas for different plane figures. Here are the steps to follow to solve this type of problem.

Rule

Determine the right area formula to be used.
Replace the variables with the known values.
Isolate the unknown variable.
Answer the question.

Here are a series of examples. The first are abstract geometry problems, while the last one is a word problem that includes a short scenario.

Example

Find the measure of the side of the following square.

A square for which the side length is sought.

See solution

Example

Find the measure of the height of the following triangle.

A triangle for which the height is sought.

See solution

Example

Find the measure of the large base of the following trapezoid.

A trapezoid for which the large base is sought.

See solution

Example

Find the measure of the apothem of the following regular hexagon.

A regular hexagon for which the apothem is sought.

See solution

Example

Find the measure of the radius of the following circle.

A circle for which the radius is sought.

See solution

Word Problem

Example

To ensure maximum safety, a school bus company wants to put glittering lights around the stop arm of its buses. This arm is formed by a rectangle and a regular octagon.

Knowing that the total area of this figure is |15.42\ \text{dm}^2,| determine how many lights can be installed on the contour of the stop arm if the company wants to install lights at every |5\ \text{cm}.|

See solution

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Word Problem

See solution

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