Question

Find the surface area of this prism.

Accepted Answer

Given prism:

To find the surface area of a given prism we have to find different surface areas separately. In a given prism, we have to find the area of three different rectangles and two triangles of similar size.

Dimension of different surfaces.

1st rectangle:

Length = $7 f t$

Width = $5 f t$

2nd rectangle:

Length = $7 f t$

Width = $4 f t$

3rd rectangle:

Length = $7 f t$

Width = $3 f t$

Two similar triangles:

Height = $3 f t$

Base = $4 f t$

Now, first we find area of 1st rectangle.

$A r e a o f r e c \tan g l e = l e n g t h \times w i d t h A r e a o f r e c \tan g l e = 7 \times 5 A r e a o f r e c \tan g l e = 35 f t^{2}$

So, the area of 1st rectangle is $35 f t^{2}$ .

Now, we find the area of the 2nd rectangle.

$A r e a o f r e c \tan g l e = l e n g t h \times w i d t h A r e a o f r e c \tan g l e = 7 \times 4 A r e a o f r e c \tan g l e = 28 f t^{2}$

So, the area of the 2nd rectangle is $28 f t^{2}$ .

Now, we find the area of 3rd rectangle.

$A r e a o f r e c \tan g l e = l e n g t h \times w i d t h A r e a o f r e c \tan g l e = 7 \times 3 A r e a o f r e c \tan g l e = 21 f t^{2}$

So, the area of the 3rd rectangle is $21 f t^{2}$ .

Now, we find the area of two similar triangles.

$A r e a o f t r i a n g l e = \frac{1}{2} \times h e i g h t \times b a s e A r e a o f t r i a n g l e = \frac{1}{2} \times 3 \times 4 A r e a o f t r i a n g l e = 6 f t^{2}$

So, the area of two similar triangles is $2 \times 6 = 12 f t^{2}$ .

$A r e a o f p r i s m = s u m o f a l l s u r f a c e a r e a s A r e a o f p r i s m = 35 + 28 + 21 + 12 A r e a o f p r i s m = 96 f t^{2}$

So, the surface area of prism is $96 f t^{2}$ .

David Weber, Talei Kunkel, Alexander Martinez and, Rebecca Shultis Solutions for Chapter: 2D and 3D Geometry Human and Natural Landscapes, Exercise 14: Practice 3

David Weber Mathematics Solutions for Exercise - David Weber, Talei Kunkel, Alexander Martinez and, Rebecca Shultis Solutions for Chapter: 2D and 3D Geometry Human and Natural Landscapes, Exercise 14: Practice 3

Questions from David Weber, Talei Kunkel, Alexander Martinez and, Rebecca Shultis Solutions for Chapter: 2D and 3D Geometry Human and Natural Landscapes, Exercise 14: Practice 3 with Hints & Solutions

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