A regular polygon has perimeter 40 and apothem 3. What is its area?

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

A regular polygon has perimeter 40 and apothem 3. What is its area?

Explanation:
For a regular polygon, you can find the area by using the apothem and the perimeter: area equals one-half times the perimeter times the apothem. Picture dividing the polygon from the center into congruent triangles; each triangle has height equal to the apothem and base equal to a side, so the total area is (1/2) times the sum of all bases (the perimeter) times the apothem. Plugging in the numbers: perimeter is 40 and the apothem is 3, so the area is (1/2) * 40 * 3 = 60. So the area is 60.

For a regular polygon, you can find the area by using the apothem and the perimeter: area equals one-half times the perimeter times the apothem. Picture dividing the polygon from the center into congruent triangles; each triangle has height equal to the apothem and base equal to a side, so the total area is (1/2) times the sum of all bases (the perimeter) times the apothem.

Plugging in the numbers: perimeter is 40 and the apothem is 3, so the area is (1/2) * 40 * 3 = 60.

So the area is 60.

More practice questions