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

Assuming each figure is a regular prism, find the missing values in the following table. Round answers to the nearest tenth where appropriate.

Accepted Answer

Given table:

To find the missing value in the above table we have to use the formula of prism which is different for different prisms.

General formula: $T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = n u m b e r o f s i d e \times (a b + b h)$

Where 'a' is the apothem, 'b' is the side length and 'h' is the height of a prism.

Now, we take rows one by one.

Row1:

In row1 prism is a pentagonal prism that means it has 5 sides. We have to find an area.

$T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = n u m b e r o f s i d e \times (a b + b h) T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = 5 \times (6.9 \times 10 + 10 \times 18) T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = 5 \times (69 + 180) T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = 1245 c m^{2}$

Row2:

In row2 prism is a hexagonal prism that means it has 6 sides. We have to find an area.

$T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = n u m b e r o f s i d e \times (a b + b h) T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = 6 \times (6.1 \times 7 + 7 \times 7) T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = 6 \times (42.7 + 49) T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = 550.2 c m^{2}$

Row3:

In row3 prism is a heptagonal prism that means it has 7 sides. We have to find an area.

$T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = n u m b e r o f s i d e \times (a b + b h) T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = 7 \times (12.5 \times 12 + 12 \times 21) T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = 7 \times (150 + 252) T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = 2814 c m^{2}$

Row4:

In row4 prism is an octagonal prism that means it has 8 sides. We have to find the height of a prism.

$T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = n u m b e r o f s i d e \times (a b + b h) 4656 = 8 \times (24.1 \times 20 + 20 \times h) \frac{4656}{8} = 482 + 20 h 582 - 482 = 20 h 100 = 20 h H e i g h t (h) = \frac{100}{20} H e i g h t (h) = 5 c m$

Row5:

In row5 prism is a decagonal prism that means it has 10 sides. We have to find the height of a prism.

$T o t a l s u r f a c e a r e a o f r e g u l a r p o y g o n a l p r i s m = n u m b e r o f s i d e \times (a b + b h) 6176 = 10 \times (24.6 \times 16 + 16 h) \frac{6176}{10} = 393.6 + 16 h 617.6 - 393.6 = 16 h 224 = 16 h H e i g h t (h) = \frac{224}{16} H e i g h t (h) = 14 c m$

Now, we put the missing value in the table.

Prism
Side length

(cm)

Apothem

(cm)

Height of prism

(cm)

Surface area

(cm²)

Pentagonal 10 6.9 18 1245

Hexagonal 7 6.1 7 550.2

Heptagonal 12 12.5 21 2814

Octagonal 20 24.1 5 4656

Decagonal 16 24.6 14 6176

Assuming each figure is a regular prism, find the missing values in the following table. Round answers to the nearest tenth where appropriate.

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