How do you calculate the area of a regular polygon with known side length?

If the side length 's' and the number of sides 'n' are known, the area can be calculated using the formula: $$A = \frac{n s^2}{4 \tan(\frac{\pi}{n})$$ .

What is the area of a regular octagon with a side length of 5 units?

Using the formula for the area of a regular polygon, the area A = $$A = \frac{n s^2}{4 \tan(\frac{\pi}{n})$$ . For an octagon (n=8), A = $$\frac{8 \times 5^2}{4 \tan(\frac{\pi}{8})} = 25 \times 2 = 50 \text{ units}^2$$ .

What is the formula for the area of a triangle?

The area A of a triangle can be calculated using the formula: $$A = \frac{1}{2} b h$$ , where 'b' is the base and 'h' is the height.

If a regular polygon has 12 sides, what is the measure of each interior angle?

The measure of each interior angle of a regular polygon can be calculated using the formula: $$\text{Interior Angle} = \frac{(n-2) \times 180}{n}$$ . For n=12, each angle = $$\frac{(12-2) \times 180}{12} = 150 \text{ degrees}$$ .

What is the area of a regular pentagon with a side length of 6 units?

Using the formula for the area of a regular polygon, the area A = $$\frac{5 \times 6^2}{4 \tan(\frac{\pi}{5})} = 61.94 \text{ units}^2$$ .

What is the significance of the apothem in calculating the area of a regular polygon?

The apothem is crucial in calculating the area of a regular polygon as it provides the height needed in the area formula: $$A = \frac{1}{2} a P$$ .

How do you find the shaded area when a square is removed from a regular polygon?

To find the shaded area, calculate the area of the regular polygon and subtract the area of the square: $$\text{Shaded Area} = \text{Area of Polygon} - \text{Area of Square}$$ .

What is the area of a regular dodecagon (12 sides) with a side length of 4 units?

Using the area formula for a regular polygon, the area A = $$\frac{12 \times 4^2}{4 \tan(\frac{\pi}{12})} = 41.57 \text{ units}^2$$ .

Resource Library

Math

Geometry

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7 2 Area Of Regular Polygons

7-2 Area of Regular Polygons

Flashcard

•

Mathematics

•

7th - 10th Grade

•

Practice Problem

•

Hard

•

CCSS

6.G.A.1, 3.MD.D.8

Standards-aligned

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15 questions

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FLASHCARD QUESTION

Front

What is the apothem of a regular polygon?

Back

The apothem is a line from the center of a regular polygon that is perpendicular to one of its sides.

FLASHCARD QUESTION

Front

What is the formula to find the area of a regular polygon?

Back

Tags

CCSS.6.G.A.1

FLASHCARD QUESTION

Front

How do you find the area of a regular pentagon?

Back

Tags

CCSS.6.G.A.1

FLASHCARD QUESTION

Front

What is the perimeter of a regular polygon?

Back

Tags

CCSS.3.MD.D.8

FLASHCARD QUESTION

Front

What is the relationship between the apothem and the radius of a regular polygon?

Back

The apothem is the shortest distance from the center to a side, while the radius is the distance from the center to a vertex. The apothem is shorter than the radius.

FLASHCARD QUESTION

Front

If the side length of a regular hexagon is 10 units, what is its perimeter?

Back

Tags

CCSS.3.MD.D.8

FLASHCARD QUESTION

Front

What is the area of a regular hexagon with an apothem of 8 units and a perimeter of 48 units?

Back

Tags

CCSS.6.G.A.1

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