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

Find the surface area of this prism.

Accepted Answer

Given us:

Given prism is an octagonal prism that has two equal octagons and eight equal rectangles. To find the area of prism we have to find the area of octagons and rectangles then sum them.

Dimension of an octagonal prism.

Two equal octagons:

Side length = $12 m m$

Apothem = $14.5 m m$

Five equal rectangles:

Length = $12 m m$

Width = $10 m m$

Now, first we find the area of two equal octagons.

$A r e a o f o c t a g o n = 8 \times \frac{1}{2} \times s i d e l e n g t h \times a p o t h e m A r e a o f o c t a g o n = 8 \times \frac{1}{2} \times 12 \times 14.5 A r e a o f o c t a g o n = 696 m m^{2}$

So, the area of two equal octagons is $2 \times 696 = 1392 m m^{2}$ .

Now we find areas of eight equal rectangles.

$A r e a o f r e c \tan g l e = l e m g t h \times w i d t h A r e a o f r e c \tan g l e = 12 \times 10 A r e a o f r e c \tan g l e = 120 m m^{2}$

So, the area of eight equal rectangles is $8 \times 120 = 960 m m^{2}$ .

Now, we find the area of a prism.

$A r e a o f p r i s m = s u m o f a r e a o f o c t a g o n s a n d r e c \tan g l e s A r e a o f p r i s m = 1392 + 960 A r e a o f r e c \tan g l e = 2352 m m^{2}$

So, the surface area of a prism is $2352 m m^{2}$ .

Find the surface area of this prism.

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