In terms of the perimeter P and apothem a, the area of a regular polygon is A = ?

Prepare for the Geometry CBE Exam with targeted resources. Access interactive quizzes and detailed explanations to master geometric concepts effectively and excel in your test!

Multiple Choice

In terms of the perimeter P and apothem a, the area of a regular polygon is A = ?

Dividing a regular polygon into congruent isosceles triangles with height equal to the apothem makes the area add up neatly. Each triangle has area (1/2) times its base (a side length) times its height (the apothem). If there are n triangles, the total area is n × (1/2) × base × a. Since the base times the number of triangles equals the perimeter P, the total becomes (1/2) × P × a. So the area in terms of the perimeter and apothem is A = (1/2) P a. The other expressions don’t fit: using P a would double the true area, adding a and P isn’t an area unit, and a^2 isn’t the correct dimensional combination for this setup.

Dividing a regular polygon into congruent isosceles triangles with height equal to the apothem makes the area add up neatly. Each triangle has area (1/2) times its base (a side length) times its height (the apothem). If there are n triangles, the total area is n × (1/2) × base × a. Since the base times the number of triangles equals the perimeter P, the total becomes (1/2) × P × a.

So the area in terms of the perimeter and apothem is A = (1/2) P a.

The other expressions don’t fit: using P a would double the true area, adding a and P isn’t an area unit, and a^2 isn’t the correct dimensional combination for this setup.

More practice questions