Name: Perimeter of a Closed Semicircular Figure
Uploaded: 2019-07-19
Duration: 2 min 24 s
Description: We know how to calculate the circumference or perimeter of a circle. Let’s watch how to calculate the perimeter of a closed semicircular figure in this video.

Question

Make a copy of this table. Assuming each figure is a regular polygon, find the missing value. Round answers to the nearest tenth where appropriate.

Polygon	Side length (cm)	Apothem	Area (cm²)
pentagon	6		61.9
hexagon	10		259.8
octagon		5	82.8
decagon	20		3077.7
hexagon		12	498.8
pentagon		30	3269.4

Accepted Answer

Given table:

Polygon Side length (cm) Apothem Area (cm²)

pentagon 6 61.9

hexagon 10 259.8

octagon 5 82.8

decagon 20 3077.7

hexagon 12 498.8

pentagon 30 3269.4

Here, we have to find the different parameters in the given table in the blank space.

The general formula of a regular polygon:

$A r e a o f p o l y g o n = n u m b e r o f s i d e \times \frac{1}{2} \times A p o t h e m \times s i d e l e n g t h$

We use this formula to find different parameters. Let take rows of table one by one to find the value of blank space.

Row1: It is a pentagon means it has 5 sides.

We have to find apothem.

$A r e a o f p o l y g o n = n u m b e r o f s i d e \times \frac{1}{2} \times a p o t h e m \times s i d e l e n g t h 61.9 = 5 \times \frac{1}{2} \times a p o t h e m \times 6 A p o t h e m = \frac{61.9 \times 2}{5 \times 6} A p o t h e m = 4.1 c m$

Row2: It is a hexagon means it has 6 sides.

We have to find apothem.

$A r e a o f p o l y g o n = n u m b e r o f s i d e \times \frac{1}{2} \times a p o t h e m \times s i d e l e n g t h 259.8 = 6 \times \frac{1}{2} \times a p o t h e m \times 10 A p o t h e m = \frac{259.8 \times 2}{6 \times 10} A p o t h e m = 8.7 c m$

Row3: It is an octagon means it has 8 sides.

We have to find side length.

$A r e a o f p o l y g o n = n u m b e r o f s i d e \times \frac{1}{2} \times a p o t h e m \times s i d e l e n g t h 82.8 = 8 \times \frac{1}{2} \times 5 \times s i d e l e n g t h S i d e l e n g t h = \frac{82.8 \times 2}{8 \times 5} S i d e l e n g t h = 4.1 c m$

Row4: It is a decagon means it has 10 sides.

We have to find apothem.

$A r e a o f p o l y g o n = n u m b e r o f s i d e \times \frac{1}{2} \times a p o t h e m \times s i d e l e n g t h 3077.7 = 10 \times \frac{1}{2} \times a p o t h e m \times 20 A p o t h e m = \frac{3077.7 \times 2}{10 \times 20} A p o t h e m = 30.8 c m$

Row5: It is a hexagon means it has 6 sides.

We have to find side length.

$A r e a o f p o l y g o n = n u m b e r o f s i d e \times \frac{1}{2} \times a p o t h e m \times s i d e l e n g t h 498.8 = 6 \times \frac{1}{2} \times 12 \times s i d e l e n g t h S i d e l e n g t h = \frac{498.8 \times 2}{6 \times 12} S i d e l e n g t h = 13.9 c m$

Row6: It is a pentagon means it has 5 sides.

We have to find side length.

$A r e a o f p o l y g o n = n u m b e r o f s i d e \times \frac{1}{2} \times a p o t h e m \times s i d e l e n g t h 3269.4 = 5 \times \frac{1}{2} \times 30 \times s i d e l e n g t h S i d e l e n g t h = \frac{3269.4 \times 2}{5 \times 30} S i d e l e n g t h = 43.6 c m$

Now we fill the table.

Polygon
Side length

(cm)

Apothem

(cm)

Area

(cm²)

Pentagon 6 4.1 61.9

Hexagon 10 8.7 259.8

Octagon 4.1 5 82.8

Decagon 20 30.8 3077.7

Hexagon 13.9 12 498.8

Pentagon 43.6 30 3269.4

Important Questions on 2D and 3D Geometry Human and Natural Landscapes

Learn and Prepare for any exam you want !

Make a copy of this table. Assuming each figure is a regular polygon, find the missing value. Round answers to the nearest tenth where appropriate. Polygon Side length (cm) Apothem Area (cm2) pentagon 6 61.9 hexagon 10 259.8 octagon 5 82.8 decagon 20 3077.7 hexagon 12 498.8 pentagon 30 3269.4

Important Questions on 2D and 3D Geometry Human and Natural Landscapes

Learn and Prepare for any exam you want !